Dr. SK Goyal Solutions for Chapter: Ellipse, Exercise 8: FILL IN THE BLANKS

The number of real tangents that can be drawn to the ellipse $3x^2+5y^2=32$ passing through $\left(3,5\right)$ is

The pole of the line $9x+2y=1$ with respect to the ellipse $3x^2+2y^2=1$ is

The points, where the normals to the ellipse $x^2+3y^2=37$ be parallel to the line $6x-5y+7=7$ is/are

If $\alpha ,\beta$ are eccentric angles of the extremities of a focal chord of an ellipse, then eccentricity of the ellipse is

The locus of mid-points of a focal chord of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is

If the length of the major axis of an ellipse is three times the length of its minor axis, its eccentricity is

The radius of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$, and having its centre $\left(0,3\right)$ is

If $A$ and $B$ are two fixed points and $P$ is a variable point such that $PA+PB=4$, then locus of $P$ is