Ellipse PYQs - Last 5 Years

The minimum length of intercept on any tangent to the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ cut by the circle $x^2+y^2=25$ is

Consider the following ellipse :
$\frac{x^2}{f\left(K^2+2 K+5\right)}+\frac{y^2}{f(K+11)}=1$, where $f(x)$ is a positive decreasing function. Then the value (values) of $K$ for which the major axis coincides with $x$-axis is

With origin as a focus and \(x=4\) as corresponding directrix, a family of ellipse are drawn. Then the locus of an end of minor axis is

A line of fixed length \(\mathrm{a}+\mathrm{b} . \mathrm{a} \neq \mathrm{b}\) moves so that its ends are always on two fixed perpendicular straight lines. The locus of a point which divides the line into two parts of length a and b is

The equation \(\mathrm{r} \cos \theta=2 \mathrm{a} \sin ^2 \theta\) represents the curve

Let f be a strictly decreasing function defined on R such that \(f(x) > 0,\forall x \in R\). Let \({{{x^2}} \over {f({a^2} + 5a + 3)}} + {{{y^2}} \over {f(a + 15)}} = 1\) be an ellipse with major axis along the y-axis. The value of 'a' can ...

If the lines joining the focii of the ellipse \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\) where \(a > b\), and an extremity of its minor axis is inclined at an angle 60\(^\circ\), then the eccentricity of the ellipse is

The tangent at point \((a\cos \theta ,b\sin \theta ),0 < \theta < {\pi \over 2}\), to the ellipse \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\) meets the x-axis at T and y-axis at T\(_1\). Then the value of $$\mathop {\min }\l...

Chords of an ellipse are drawn through the positive end of the minor axis. Their midpoint lies on

AB is a variable chord of the ellipse \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\). If AB subtends a right angle at the origin O, then \({1 \over {O{A^2}}} + {1 \over {O{B^2}}}\) equals to