Ellipse - Coordinate Geometry - Mathematics Previous Year Questions

If p is any point on the ellipse \({{{x^2}} \over {36}} + {{{y^2}} \over {16}} = 1\), and S and S' are the foci, then \(PS + PS' =\)

If the area of the auxillary circle of the ellipse \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1(a > b)\) is twice the area of the ellipse, then the eccentricity of the ellipse is

If the length of the major axis of an ellipse is 3 times the length of the minor axis, then its eccentricity is

The points on the ellipse \(16 x^2+9 y^2=400\) at which the ordinate decreases at the same rate at which the abscissa increases are

If an ellipse has an equation in the standard form and it passes through the points \(\left(\frac{5}{2}, \frac{\sqrt{6}}{4}\right)\) and \(\left(-2, \frac{\sqrt{15}}{5}\right)\) then the length of its latus rectum is

$$\text { The area of the region enclosed by the curve }\left\{(x, y): 4 x^2+25 y^2=100\right\} \text { is }$$

The equation of an ellipse, whose focus is \((1,0)\), directrix is \(x=4\) and whose eccentricity is a root of the quadratic equation \(2 x^2-3 x+1=0\), is

The length of the latus rectum of the curve represented by $x=3(\cos t+\sin t)$ and $y=4(\cos t-\sin t)$ is:

If the two ends of the major axis of an ellipse are $(5,0)$ and $(-5,0)$ and one focus lies on the line $3 x-5 y-9=0$, then its equation is