The range of r for which circles (x + 1)² + (y + 2)² = r² and x² + y² – 4x – 4y + 4 = 0 coincide at two distinct points

An ellipse whose length of minor axis is equal to half of length between foci, then eccentricity is

If hyperbola and ellipse x² – y²cosec²q = 5 and ellipse x²cosec²q + y² = 5 has eccentricity e_H and e_e respectively and e_H = $\sqrt[]{7}{e}_e$ <!-- [if gte mso 9]><xml> </xml><![endif]-->, then q is equal to

A parabola has vertex (2, 3), equation of directrix is 2x – y = 1 and equation of ellipse is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,e=\frac{1}{\sqrt[]{2}}$ <!-- [if gte mso 9]><xml> </xml><![endif]--> and ellipse passing through focur of parabola then square of length of latus rectum of ellipse is

The locus of the point of intersection of the lines $\left(\sqrt[]{3}\right)kx+ky-4\sqrt[]{3}=0and\sqrt[]{3}x-y-4\left(\sqrt[]{3}\right)k$ = 0 is a conic, whose eccentricity is…………………

Let A(1, 4) and B(1, -5) be two points. Let P be a point on the circle ${\left(x-1\right)}^2+{\left(y-1\right)}^2=1$ <!-- [if gte mso 9]><xml> </xml><![endif]--> such that ${\left(PA\right)}^2+{\left(PB\right)}^2$ <!-- [if gte mso 9]><xml> </xml><![endif]--> have a maximum value, then the points P, A and B lie on: