Question

The number of normals can be drawn from any point to an ellipse are

• A. Five
• B. Four
• C. Three
• D. None of these

Answer 1

The correct option is B Four

The equation of the normals of slope $m$ to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ are given by

$y=mx\mp \frac{m(a^2-b^2)}{\sqrt{a^2+b^2{m}^2}}$ at the points $(\pm \frac{a^2}{\sqrt{a^2+b^2{m}^2}},\pm \frac{m{b}^2}{\sqrt{a^2+b^2{m}^2}})$

Therefore, number of normals can be drawn from any point to an ellipse are four.

Hence, B is the correct answer.