Question

If p and q are the x and y intercepts respectively of the line passing through the points \( (a \cos \alpha, b \sin \alpha) \) and \( (a \cos \beta, b \sin \beta) \), then:

• A. \( \frac{a^2 + b^2}{p^2} = \frac{a^2 + b^2}{q^2} \)
• B. \( \frac{a^2 + b^2}{p^2} = \frac{a^2 + b^2}{q^2} \)
• C. \( \frac{a^2 + b^2}{p^2} = \frac{a^2 + b^2}{q^2} \)
• D. \( \frac{a^2 + b^2}{p^2} = \frac{a^2 + b^2}{q^2} \)

Hint:

In problems involving intercepts and trigonometric identities, use the geometric approach to derive the relation between the intercepts and the coordinates.

Answer 1

The Correct Option is C

Using the geometry of the given line passing through the points and the intercept form, we calculate the ratio between \( p^2 \) and \( q^2 \). The correct result is \( \frac{a^2 + b^2}{p^2} = \frac{a^2 + b^2}{q^2} \).