$AB$ is a chord of the parabola $y^{2} = 4ax$ with vertex $A,\ BC$ is drawn perpendicular to $AB$ meeting the axis at $C$. The projection of $BC$ on the axis of the parabola is

Question

Dr. Abubacker · Accepted Answer

(c)
Given equation of parabola is $y^{2} = 4ax$
Let the coordinates of $B$ are $\left( {at}^{2},\ 2at \right)$
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Slope of $AB = \frac{2}{t}$
Since, $BC$ is perpendicular to $AB$
So, slope of $BC = - \frac{t}{2}$
Equation of $BC$ is $y - 2at = - \frac{t}{2}(x - {at}^{2})$
This line meets to the $x$-axis at point $C$
Put $y = 0 \Rightarrow x = 4a + {at}^{2}$
So, distance $CD = 4a + {at}^{2} - {at}^{2} = 4a$

Q. $AB$ is a chord of the parabola $y^{2} = 4ax$ with vertex $A,\ BC$ is drawn perpendicular to $AB$ meeting the axis at $C$. The projection of $BC$ on the axis of the parabola is

Explanation

Reviewed by Dr. Abubacker

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