If the tangent to the parabola $y^{2} = ax$ makes an angle of $45^{{^\circ}}$ with $x$-axis, then the point of contact is

Question

Dr. Abubacker · Accepted Answer

(d)
Given parabola $y^{2} = ax$
$ie,\ y^{2} = 4\left( \frac{a}{4} ight)x$ …(i)
let point of contact is $(x_{1},\ y_{1})$, then equation of tangent is
$yy_{1} = \frac{a}{2}(x + x_{1})$
Here, $m = \frac{a}{2y_{1}} = 	an 45^{{^\circ}}$
$\Rightarrow \frac{a}{2y_{1}} = 1 \Rightarrow y_{1} = \frac{a}{2}$
From Eq. (i), $x_{1} = \frac{a}{4}$
$	herefore$ Point of contact is $\left( \frac{a}{4},\ \frac{a}{2} ight)$

Q. If the tangent to the parabola $y^{2} = ax$ makes an angle of $45^{{^\circ}}$ with $x$-axis, then the point of contact is

Explanation

Reviewed by Dr. Abubacker

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