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Mathematics - Coordinate Geometry Mixed Question with Solution | TestHub

MathematicsCoordinate Geometry MixedCoordinate Geometry MixedMedium2 minQB

MathematicsMediumsingle choice

Consider an ellipse $\frac{x ^{2}}{4} + y^{2} = α$ (where $α$ is a parameter > 0) and a parabola $y^{2} = 8 x$ . If a common tangent to the ellipse and the parabola meets the coordinate axes at A and B respectively, then Locus of midpoints of AB is

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Solution:

Equation of tangent to $y^{2} = 8 x$ is $y t - x - 2 t^{2} = 0$ . It meets the x-axis at $A (- 2 t^{2}, 0)$ and the y-axis at $B (0, 2 t)$ . Midpoint of $AB : (h, k) = (- t^{2}, t) \Rightarrow k^{2} = - h$ . Locus: $y^{2} = - x$ .

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

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