The foci of the ellipse $25{(x + 1)^2} + 9{(y + 2)^2} = 225$ are at

Let a tangent to the Curve $9 x^2+16 y^2=144$ intersect the coordinate axes at the points $A$ and $B$. Then, the minimum length of the line segment $A B$ is $.........$

The equation of an ellipse whose focus $(-1, 1)$, whose directrix is $x - y + 3 = 0$ and whose eccentricity is $\frac{1}{2}$, is given by

The equations of the common tangents to the ellipse, $ x^2 + 4y^2 = 8 $ $\&$  the parabola $y^2 = 4x$  can be

For the ellipse $\frac{{{x^2}}}{{64}} + \frac{{{y^2}}}{{28}} = 1$, the eccentricity is

The line $12 x \,\cos \theta+5 y \,\sin \theta=60$ is tangent to which of the following curves?