Question

The equation of the normal to the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ at the positive end of a latus rectum is

• A. x+ey+e³a = 0
• B. x-ey-e³a= 0
• C. x – ey – e²a = 0
• D. None of these

Answer 1

Answer: (B)

x-ey-e³a= 0

Answer 2

The equation of the normal at (x₁, y₁) to the given ellipse is $\frac{a^{2}x}{x_{1}} - \frac{b^{2}y}{y_{1}} = a^{2} - b^{2}$

Here x₁ = ae and y₁ = b²/a

So, the equation of the normal at positive end of the latus rectum is

$\frac{a^{2}x}{x_{1}} - \frac{b^{2}y}{b^{2}/a} = a^{2}e^{2} \Rightarrow \frac{ax}{e} - ay = a^{2}e^{2}$⇒ x - ey - e³a = 0