Question

A perpendicular is dropped on the transverse axis of the hyperbola $\frac{x^2}{49}-\frac{y^2}{36}=1$ from its asymptote. What will be the product of the segments of this line intercepted between the point and the curve?

• A. $36$
• B. $6$
• C. $49$
• D. $7$

Answer 1

The correct option is A $36$

Given: Hyperbola: $\frac{x^2}{49}-\frac{y^2}{36}=1,$

Here $a=7,b=6$

From any point on the asymptote, if a perpendicular is drawn to the transverse axis, then the product of the segments of the line intercepted between the point and the curve is always equal to the square of semi-conjugate axis

$\therefore$ Product of the segments $=b^2=36$