Question:
The condition that the line \( \frac{x}{p} + \frac{y}{q} = 1 \) be normal to the parabola \( y^2 = 4ax \) is
The condition that the line \( \frac{x}{p} + \frac{y}{q} = 1 \) be normal to the parabola \( y^2 = 4ax \) is
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To find the condition for a line to be normal to a curve, use the derivative of the curve to find the slope at the point of tangency.
Updated On: Jan 12, 2026
- \( p^3 = 2a p^2 + a^3 \)
- \( p^3 = 2a p^2 + 2a^2 p \)
- \( p^3 = 2a^2 + a^3 \)
- \( p^3 = 2a p^2 + 2a^3 \)
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The Correct Option is B
Solution and Explanation
The condition for the line to be normal to the parabola is derived by using the derivative and the normal line equation.
Final Answer: \[ \boxed{p^3 = 2a p^2 + 2a^2 p} \]
Final Answer: \[ \boxed{p^3 = 2a p^2 + 2a^2 p} \]
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