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 y²=4 ax passing through D is (α+β √(2), 0), where α and β are rational numbers, then (α)/(β²) is equal to:

Coordinate Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 8 Apr, Evening shift · Q4758

JEE Main 20238 Apr, Evening shiftMathematicsHardCoordinate Geometry478× since 2002

Let

\mathrm{A}(0,1), \mathrm{B}(1,1)

and

\mathrm{C}(1,0)

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

\mathrm{D}

. If the focus of the parabola

y^{2}=4 \mathrm{ax}

passing through

\mathrm{D}

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

, where

\alpha

and

\beta

are rational numbers, then

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

is equal to :