Mathematics - Circle Question with Solution | TestHub

MathematicsCircleRadical Axis & Radical Centre, Coaxial system of circles, Orthogonality of two circlesMedium2 minQB

MathematicsMediumsingle choice

Two circles through $(0, a)$ and $(0, - a)$ intersect orthogonally and both touch $y = m x + c$ . What relation holds?

Options:

Answer:

Solution:

Write the circles as $x^{2} + y^{2} + 2 t a x - a^{2} = 0$ . Orthogonality gives $t_{1} t_{2} = - 1$ . Tangency to the line yields a quadratic in $t$ whose root product is $(a^{2} (1 + m^{2}) - c^{2}) / a^{2} = - 1$ , hence C.

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Radical Axis & Radical Centre, Coaxial system of circles, Orthogonality of two circles

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...