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If the ellipse x^2/a^2+y^2/b^2=1 (b > a)...

If the ellipse `x^2/a^2+y^2/b^2=1 (b > a)` and the parabola `y^2 = 4ax` cut at right angles, then eccentricity of the ellipse is (a) `(3)/(5)` (b) `(2)/(3)` (c) `(1)/(sqrt(2))` (d) `(1)/(2)`

A

`(3)/(5)`

B

`(2)/(3)`

C

`(1)/(sqrt(2))`

D

`(1)/(2)`

Text Solution

AI Generated Solution

To solve the problem, we need to find the eccentricity of the ellipse given that it intersects the parabola at right angles. ### Step-by-Step Solution: 1. **Identify the equations**: The equation of the ellipse is given by: \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \quad (b > a) ...
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