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
$AB$ 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
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Parametric form simplifies most parabola geometry problems.
Updated On: Apr 23, 2026
- $a$
- $2a$
- $4a$
- $8a$
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The Correct Option is C
Solution and Explanation
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: \[ 4a \] Conclusion:
Answer = $4a$
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: \[ 4a \] Conclusion:
Answer = $4a$
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