The sum of the focal distances of any point on the conic $\frac{x^2}{25} + \frac{y^2}{16} = 1$ is

Given the base of a triangle and the sum of its other two sides,the locus of the center of its incircle is:

The locus of the point of intersection of perpendicular tangents to the ellipse $\frac{x^2}{25} + \frac{y^2}{16} = 1$ is:

If $S$ and $S^{\prime}$ are the foci of the ellipse $\frac{x^2}{18}+\frac{y^2}{9}=1$ and $P$ is a point on the ellipse,then $\min \left(SP \cdot S^{\prime}P\right) + \max \left(SP \cdot S^{\prime}P\right)$ is equal to:

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

The eccentricity of the conic $16x^2 + 7y^2 = 112$ is