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Mathematics - Coordinate Geometry Mixed Question with Solution | TestHub

MathematicsCoordinate Geometry MixedCoordinate Geometry MixedMedium2 minQB

MathematicsMediumsingle choice

Common tangents from K are drawn to the parabola $y^{2} = 4 x$ and the ellipse $3 x^{2} + 8 y^{2} = 48$ touching the parabola at A and B and the ellipse at C and D. The area of the quadrilateral ABCD is equal to

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Solution:

Points of contact on the parabola: $A (8, 42), B (8, - 42)$ , so $A B = 82$ . Points of contact on the ellipse: $C, D = (- 2, \pm \frac{3}{2})$ , so $C D = 32$ . The two chords are the parallel lines $x = 8$ and $x = - 2$ , distance 10 apart. Area of quadrilateral $A BC D = \frac{1}{2} (A B + C D) \times 10 = \frac{1}{2} (82 + 32) \times 10 = 552$ .

Stream:JEESubject:MathematicsTopic:Coordinate Geometry MixedSubtopic:Coordinate Geometry Mixed

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