Question

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

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

Hint:

Parametric form simplifies most parabola geometry problems.

Answer 1

The Correct Option is C

Understanding the Concept: Parametric form of parabola

Step 1: Vertex = (0,0), point $B = (at^2, 2at)$.

Step 2: Slope of $AB$: \[ \frac{2at}{at^2} = \frac{2}{t} \]

Step 3: Perpendicular slope = $-\frac{t}{2}$.

Step 4: Equation of $BC$ through $B$ and meet x-axis.

Step 5: Projection on axis simplifies to: \[ 4a \] Final Answer:
Answer = $4a$