The locus of the point $P(x, y)$ satisfying the relation $\sqrt{(x - 3)^2 + (y - 1)^2} + \sqrt{(x + 3)^2 + (y - 1)^2} = 6$ is

If the length of the latus rectum of an ellipse is $4 \ units$ and the distance between a focus and its nearest vertex on the major axis is $\frac{3}{2} \ units$,then its eccentricity is?

The curve represented by $\frac{x^2}{12-\alpha} + \frac{y^2}{\alpha-10} = 1$ is

The equation of the normal at the point $(2, 3)$ on the ellipse $9x^2 + 16y^2 = 180$ is:

The eccentricity of the ellipse $x^2+4 y^2+2 x+16 y+13=0$ is

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