Mathematics › Parabola
Parabola Questions
193 questions across 9 subtopics — with step-by-step solutions.
Chord of Contact(3)
Chord with given Middle Point(4)
Chords(27)
- Let and be two distinct points on the para... | Mathematics | TestHub
- Let be the focus of the parabola and let b... | Mathematics | TestHub
- The chord of the parabola , where one end... | Mathematics | TestHub
- Paragraph: Let be a focal chord of the par... | Mathematics | TestHub
- Paragraph: Let be a focal chord of the par... | Mathematics | TestHub
- Through the vertex of a parabola , chords... | Mathematics | TestHub
- Letandbe distinct points on the parabolasu... | Mathematics | TestHub
- Let be the focus of the parabola and be th... | Mathematics | TestHub
- The length of the chord of the parabolahav... | Mathematics | TestHub
- If one end of a focal chord of the parabol... | Mathematics | TestHub
- If one end of a focal chordof the parabola... | Mathematics | TestHub
- Let the latus rectum of the parabola be th... | Mathematics | TestHub
- Letbe a parabola with focus.Let the tangen... | Mathematics | TestHub
- If the-intercept of a focal chord of the p... | Mathematics | TestHub
- Let be a focal chord of the parabola of le... | Mathematics | TestHub
- Let be the length of the common chord of t... | Mathematics | TestHub
- If the line intersects the parabola at the... | Mathematics | TestHub
- Let be the parabola and be its focus. Let... | Mathematics | TestHub
- Let the focal chord of the parabola make a... | Mathematics | TestHub
- Let be a point on the parabola and PQ be a... | Mathematics | TestHub
- Let be a trapezium whose vertices lie on t... | Mathematics | TestHub
- Let the point of the focal chord of the pa... | Mathematics | TestHub
- The number of focal chords of length 4 / 7... | Mathematics | TestHub
- The length of the chord of the parabola x^... | Mathematics | TestHub
- Assertion : PQ is a chord of the parabola... | Mathematics | TestHub
- Through the vertex ' O ' of parabola y^{2}... | Mathematics | TestHub
- If AFB is a focal chord of the parabola \m... | Mathematics | TestHub
General(68)
- A variable circle passes through the fixed... | Mathematics | TestHub
- Let be the point and a point on the locus... | Mathematics | TestHub
- Paragraph:Read the following passage and a... | Mathematics | TestHub
- The locus of the vertices of the family of... | Mathematics | TestHub
- Paragraph:Read the following passage and a... | Mathematics | TestHub
- Axis of a parabola is and vertex and focus... | Mathematics | TestHub
- A parabola has the origin as its focus and... | Mathematics | TestHub
- The line is rotated through an angle in th... | Mathematics | TestHub
- Let be any point on the parabola . Let be... | Mathematics | TestHub
- The length of the latus-rectum of the para... | Mathematics | TestHub
- The area of triangle formed by the lines j... | Mathematics | TestHub
- Letbe the vertex andbe any point on the pa... | Mathematics | TestHub
- Ifbe a double ordinate of the parabola,whe... | Mathematics | TestHub
- The parabola having its focus at (3,2) and... | Mathematics | TestHub
- The locus of the point of intersection of... | Mathematics | TestHub
- Two parabolas with a common vertex and wit... | Mathematics | TestHub
- Letandbe two points on the parabola,and le... | Mathematics | TestHub
- If the area of the triangle whose one vert... | Mathematics | TestHub
- Axis of a parabola lies along-axis. If its... | Mathematics | TestHub
- Suppose a parabolahas twointercepts, one p... | Mathematics | TestHub
- Letandbe points on the parabola,Letbe chos... | Mathematics | TestHub
- The locus of a point which divides the lin... | Mathematics | TestHub
- The length of the latus rectum of the para... | Mathematics | TestHub
- Forlet the curvesandintersect at originand... | Mathematics | TestHub
- The area (in sq. units) of an equilateral... | Mathematics | TestHub
- Letbe a variable point on the parabolaThen... | Mathematics | TestHub
- The locus of the mid-point of the line seg... | Mathematics | TestHub
- The length of the latus rectum of a parabo... | Mathematics | TestHub
- If the length of the latus rectum of a par... | Mathematics | TestHub
- If vertex of parabola isand equation of it... | Mathematics | TestHub
- Letbe a parabola with vertexand focusandbe... | Mathematics | TestHub
- Letbe a conic. Letbe the focus andbe the p... | Mathematics | TestHub
- If the equation of the parabola, whose ver... | Mathematics | TestHub
- If vertex of a parabola is and the equatio... | Mathematics | TestHub
- The parabolas :andintersect on the line. I... | Mathematics | TestHub
- Let and be three points on the parabola an... | Mathematics | TestHub
- If the shortest distance of the parabolafr... | Mathematics | TestHub
- Let PQ be a chord of the parabola and the... | Mathematics | TestHub
- The maximum area of a triangle whose one v... | Mathematics | TestHub
- Let a conic pass through the point and , b... | Mathematics | TestHub
- Let the length of the focal chord PQ of th... | Mathematics | TestHub
- Suppose is a focal chord of the parabola o... | Mathematics | TestHub
- The axis of a parabola is the line and its... | Mathematics | TestHub
- Let the parabola , meet the coordinate axe... | Mathematics | TestHub
- Let the shortest distance from , to the pa... | Mathematics | TestHub
- The axis of a parabola is the line and its... | Mathematics | TestHub
- The radius of the smallest circle which to... | Mathematics | TestHub
- Let the focal chord of the parabola make a... | Mathematics | TestHub
- Let the parabola , meet the coordinate axe... | Mathematics | TestHub
- Let A and B be the two points of intersect... | Mathematics | TestHub
- If the equation of the parabola with verte... | Mathematics | TestHub
- Two parabolas have the same focus and thei... | Mathematics | TestHub
- If the equation of the parabola with verte... | Mathematics | TestHub
- Let the point of the focal chord of the pa... | Mathematics | TestHub
- The focus of the parabola is the centre of... | Mathematics | TestHub
- If the line intersects the parabola at the... | Mathematics | TestHub
- Let P be the parabola, whose focus is and... | Mathematics | TestHub
- Let be a point on the parabola and PQ be a... | Mathematics | TestHub
- A line passing through the point , touches... | Mathematics | TestHub
- Let be a trapezium whose vertices lie on t... | Mathematics | TestHub
- If parabola with focus \left(\frac{2}{5},... | Mathematics | TestHub
- \sqrt{\mathrm{x}}+\sqrt{\mathrm{y}}=1 is a... | Mathematics | TestHub
- A parabola is drawn through two given poin... | Mathematics | TestHub
- Consider the parabola y^{2}=4 x . Let P an... | Mathematics | TestHub
- OAB is a sector of a circle of radius R in... | Mathematics | TestHub
- Points \mathrm{A}, \mathrm{B}, \mathrm{C}... | Mathematics | TestHub
- If the line x-1=0 is the directrix of the... | Mathematics | TestHub
- A parabola is drawn through two given poin... | Mathematics | TestHub
Line and parabola(3)
Miscellaneous/Mixed(58)
- Match the column. Normals at are drawn to... | Mathematics | TestHub
- Equation of common tangent of is | Mathematics | TestHub
- Paragraph:Consider the circle and the para... | Mathematics | TestHub
- Paragraph:Consider the circle and the para... | Mathematics | TestHub
- Statement I The curve is symmetric with re... | Mathematics | TestHub
- Consider the two curves , then | Mathematics | TestHub
- If the equations of the pairs of opposite... | Mathematics | TestHub
- Let be a normal to the parabola . If passe... | Mathematics | TestHub
- Consider the parabola . Let be the area of... | Mathematics | TestHub
- The common tangents to the circleand the p... | Mathematics | TestHub
- If the normal of the paraboladrawn at the... | Mathematics | TestHub
- Let P be the point on the parabolawhich is... | Mathematics | TestHub
- Normals drawn toat the points where it is... | Mathematics | TestHub
- Consider the region and . Let be the famil... | Mathematics | TestHub
- Letdenote the parabolaLet, and letandbe tw... | Mathematics | TestHub
- Consider the region and . Let be the famil... | Mathematics | TestHub
- A normal is drawn at the point to the para... | Mathematics | TestHub
- Consider the parabola. Letbe the focus of... | Mathematics | TestHub
- The equation of a common tangent to the pa... | Mathematics | TestHub
- Letbe a point on the parabola, where. The... | Mathematics | TestHub
- A normal with slope is drawn from the poin... | Mathematics | TestHub
- If the line y-\sqrt{3} x+3=0 cuts the para... | Mathematics | TestHub
- If the parabola y=(a-b) x^{2}+(b-c) x+(c-a... | Mathematics | TestHub
- The number of point(s) (x, y) (where x and... | Mathematics | TestHub
- If 2 p^{2}-3 q^{2}+4 p q-p=0 and a variabl... | Mathematics | TestHub
- The ends of the latus rectum of the conic... | Mathematics | TestHub
- The equation of the line of the shortest d... | Mathematics | TestHub
- The number of focal chords of length 4 / 7... | Mathematics | TestHub
- The locus of point of intersection of any... | Mathematics | TestHub
- If the line y-\sqrt{3} x+3=0 cuts the para... | Mathematics | TestHub
- Consider the parabola x^{2}+4 y=0 . Let p=... | Mathematics | TestHub
- The Cartesian equation of the curve whose... | Mathematics | TestHub
- If x+k=0 is equation of directrix to parab... | Mathematics | TestHub
- If t is the parameter for one end of a foc... | Mathematics | TestHub
- If one end of the diameter of a circle is... | Mathematics | TestHub
- The point P on the parabola y^{2}=4 a x fo... | Mathematics | TestHub
- The locus point of intersection of tangent... | Mathematics | TestHub
- Let \mathrm{A}\left(0,(2), \mathrm{B}\righ... | Mathematics | TestHub
- The coordinates of the point on the parabo... | Mathematics | TestHub
- Slope of tangent to x^{2}=4 y from (-1,-1)... | Mathematics | TestHub
- If the angle between the asymptotes of hyp... | Mathematics | TestHub
- Consider two concentric circle \mathrm{C}_... | Mathematics | TestHub
- If there exists exactly one point in x-y p... | Mathematics | TestHub
- If point D is (\mathrm{a}, \mathrm{b}) , V... | Mathematics | TestHub
- Let r=1 for C , and \left(x_{1}, y_{1}\rig... | Mathematics | TestHub
- If AFB is a focal chord of the parabola y^... | Mathematics | TestHub
- Let f(x)=\lim _{n \rightarrow \infty} \fra... | Mathematics | TestHub
- Let P and Q be the end points of the latus... | Mathematics | TestHub
- If a variable tangent of the hyperbola \fr... | Mathematics | TestHub
- If e is the eccentricity of the hyperbola... | Mathematics | TestHub
- A straight line through \mathrm{A}(6,8) me... | Mathematics | TestHub
- The point (1,2) is one extremity of focal... | Mathematics | TestHub
- The length of the chord of the parabola x^... | Mathematics | TestHub
- If line y=2 x+\frac{1}{4} is tangent to y^... | Mathematics | TestHub
- If at x=1, y=2 x tangent to the parabola y... | Mathematics | TestHub
- Shortest distance between the line y-x=1 a... | Mathematics | TestHub
- If the lines (y-b)=m_{1}(x+a) and (y-b)=m_... | Mathematics | TestHub
- The coordinates of the point on the parabo... | Mathematics | TestHub
Normal to Parabola(4)
Tangent to Parabola(22)
- The equation of a tangent to the parabola... | Mathematics | TestHub
- The tangent and the normal to the parabola... | Mathematics | TestHub
- Statement 1: is always a tangent to the pa... | Mathematics | TestHub
- Statement : An equation of a common tangen... | Mathematics | TestHub
- Statement-1: The line meets the parabola,... | Mathematics | TestHub
- If the line touches the parabola then find... | Mathematics | TestHub
- Statement-1: The slope of the tangent at a... | Mathematics | TestHub
- The locus of the foot of perpendicular dra... | Mathematics | TestHub
- Paragraph: Let be nonzero real numbers. Le... | Mathematics | TestHub
- Paragraph: Let be nonzero real numbers. Le... | Mathematics | TestHub
- If the tangent to the conic,attouches the... | Mathematics | TestHub
- Suppose that the foci of the ellipsearewhe... | Mathematics | TestHub
- Columns 1, 2 and 3 contain conics, equatio... | Mathematics | TestHub
- Letbe a point on the parabola. If the dist... | Mathematics | TestHub
- Tangent and normal are drawn aton the para... | Mathematics | TestHub
- Let be three points in the -plane. Suppose... | Mathematics | TestHub
- The radius of the smallest circle which to... | Mathematics | TestHub
- A line passing through the point , touches... | Mathematics | TestHub
- Let be the radius of the circle, which tou... | Mathematics | TestHub
- Points lie on the parabola . Tangents to t... | Mathematics | TestHub
- Two tangents are drawn from point (1,4) to... | Mathematics | TestHub
- If the tangent at to the curve touches the... | Mathematics | TestHub
Tangents & Normals(4)
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