Question

The equation of normal at the point (0, 3) of the ellipse $9x^{2} + 5y^{2} = 45$is

• A. $y - 3 = 0$
• B. $y + 3 = 0$
• C. x-axis
• D. y-axis

Answer 1

Answer: (D)

y-axis

Answer 2

For $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$, equation of normal at point $(x_{1},y_{1})$, is

$\frac{(x - x_{1})a^{2}}{x_{1}} = \frac{(y - y_{1})b^{2}}{y_{1}}$

Here, $(x_{1},y_{1}) = (0,3)$ and $a^{2} = 5$, $b^{2} = 9$,

Therefore $\frac{(x - 0)}{0}.5 = \frac{(y - 3)}{3}.9$or $x = 0$ i.e., y-axis