Question

If \( \text{line} \, y = mx + c \) is a normal to the ellipse \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \] then \( c^2 \) is equal to

• A. \( a^2 + b^2 \)
• B. \( a^2 - b^2 \)
• C. \( b^2 - a^2 \)
• D. \( a^2 + b^2 \)

Hint:

The equation of a normal to an ellipse involves both the center and the semi-major and semi-minor axes of the ellipse.

Answer 1

The Correct Option is B

Using the equation of the ellipse and the normal line, the relationship between the semi-major and semi-minor axes is derived to obtain the value of \( c^2 \).