Tangents are drawn from points onthe circle $x^2 + y^2 = 49$ to the ellipse $\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{24}} = 1$ angle between the tangents is

  • A

    $\frac{\pi }{4}$

  • B

    $\frac{\pi }{2}$

  • C

    $\frac{\pi }{3}$

  • D

    $\frac{\pi }{8}$

Similar Questions

In the ellipse, minor axis is $8$ and eccentricity is $\frac{{\sqrt 5 }}{3}$. Then major axis is

Let $E_1: \frac{x^2}{9}+\frac{y^2}{4}=1$ be an ellipse. Ellipses $E_i$ 's are constructed such that their centres and eccentricities are same as that of $E _1$, and the length of minor axis of $E _{ i }$ is the length of major axis of $E _{ i +1}( i \geq 1)$. If $A _{ i }$ is the area of the ellipse $E _{ i }$, then $\frac{5}{\pi}\left(\sum_{ i =1}^{\infty} A _{ i }\right)$, is equal to _____

  • [JEE MAIN 2025]

The equation to the locus of the middle point of the portion of the tangent to the ellipse $\frac{{{x^2}}}{{16}}$$+$ $\frac{{{y^2}}}{9}$ $= 1$  included between the co-ordinate axes is the curve :

Find the equation of the ellipse, with major axis along the $x-$ axis and passing through the points $(4,\,3)$ and $(-1,\,4)$

Let $P$ be a variable point on the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ with foci ${F_1}$ and ${F_2}$. If $A$ is the area of the triangle $P{F_1}{F_2}$, then maximum value of $A$ is

  • [IIT 1994]