Q. Angle between tangents drawn from the point $(5,\ 4)$ to the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1$, is
A) $60{^\circ}$
B) $90{^\circ}$
C) $120{^\circ}$
D) $45{^\circ}$
Explanation
(b)
Equation of director circle of the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1$ is
$x^{2} + y^{2} = 25 + 16$
$\Rightarrow x^{2} + y^{2} = 41$
$\because$ The given point $(5,\ 4)$ lies on the director circle, therefore the tangents are drawn from this points to the ellipse makes an angle $90{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.