The locus of a variable point whose distance from $(-2, 0)$ is $\frac{2}{3}$ times its distance from the line $x = - \frac{9}{2}$, is
Ellipse
Parabola
Hyperbola
None of these
If the line $x\cos \alpha + y\sin \alpha = p$ be normal to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$, then
If the co-ordinates of two points $A$ and $B$ are $(\sqrt{7}, 0)$ and $(-\sqrt{7}, 0)$ respectively and $P$ is any point on the conic, $9 x^{2}+16 y^{2}=144,$ then $PA + PB$ is equal to
If $y = mx + c$ is tangent on the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$, then the value of $c$ is
Eccentricity of the ellipse $4{x^2} + {y^2} - 8x + 2y + 1 = 0$ is
In an ellipse, the distance between its foci is $6$ and minor axis is $8.$ Then its eccentricity is :