Question

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

• A. $a$
• B. $2a$
• C. $4a$
• D. $8a$

Answer 1

The correct option is C $4a$

In $△ABD$, we have $\tan \theta =\frac{y}{x}$
In $△BCD$, we have $\tan ({90}^o-\theta )=\frac{y}{CD}$
$\Rightarrow CD=y\tan \theta =\frac{y^2}{x}=\frac{4ax}{x}=4a$