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 $y^2 = 4ax$ 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 Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 8 April 2023, Shift 2, Maths Q12

Question 12 of 90 in this shift, Maths question 12 of 30, Section A.

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 = 4ax

passing through

D

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

, where

\alpha

and

\beta

are rational numbers, then

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

is equal to

Official answer

Option 3

NTA final key.