Hyperbola
Product of Perpendiculars
Premium Question
Grade 11
Question:
The product of the lengths of the perpendiculars from foci on any tangent to the hyperbola $\frac{x^2}{4} - \frac{y^2}{3} = 1$ is:
(1) $3$
(2) $4$
(3) $12$
(4) $\frac{4}{3}$
Step-by-Step Solution
Key Concept: For any conic, product of perpendicular distances from foci to tangent equals $b^2$. Here $b^2 = 3$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)