Let $ A(0,1), B(1,1) $ and $ C(1,0) $ be the mid-points of the sides of a triangle with incentre at the point $ D $. If the focus of the parabola $ y^{2}=4 a x $ passing through $ D $ is $ (\alpha+\beta \sqrt{2}, 0) $, where $ \alpha $ and $ \beta $ are rational numbers, then $ \frac{\alpha}{\beta^{2}} $ is equal to

JEE MATHEMATICS MCQ: PARABOLA

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Analyzing +4 | -1

Let

A(0,1), B(1,1)

and

C(1,0)

be the mid-points of the sides of a triangle with incentre at the point

D

. If the focus of the parabola

y^{2}=4 a x

passing through

D

(\alpha+\beta \sqrt{2}, 0)

, where

\alpha

and

\beta

are rational numbers, then

\frac{\alpha}{\beta^{2}}

is equal to

View answer and explanation

Correct option: A

Option A (8) is correct because after finding the incenter and the 'a' value of the parabola, we calculate the focus and then compute the required ratio.

JEE MATHEMATICS MCQ: PARABOLA

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