Question

What is the equation of normal to the ellipse
$\frac{x^2}{25}+\frac{y^2}{16}=2\text{at}(5,4).$

• A. 5x + 4y = 41
• B. 5x - 4y = 9
• C. 4x - 5y = 0
• D. 4x + 5y = 40

Answer 1

The correct option is B

5x - 4y = 9

The equation of normal to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is given by
$\frac{a^{2}x}{x_1}-\frac{b^{2}y}{y_1}=(a^2-b^2)$
But the given equation of ellipse has 2 on RHS. We will divide by 2 throughout to get the values of $a^{2}and{b}^2$
$\Rightarrow a^2=50\text{and}{b}^2=32\Rightarrow \text{Equation of normal is}\frac{50x}{5}-\frac{32y}{4}=50-32=18or10x-8y=18or5x-4y=9$