If ordinate $PQ$ of a hyperbola be produced to $R$ so that $PR$ is equal to either of the focal radii of $Q,$ then the locus of $R$ is

The distance from foci of $\frac{x^2}{9}+\frac{y^2}{25}=1$ to any point $(a, b)$ on the ellipse is

If the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ passes through the intersection of $7x+13y-87=0$ and $5x-8y+7=0$ and its latus rectum is $\frac{32\sqrt{2}}{5},$ then the values of $\text{'}a\text{'}$ and $\text{'}b\text{'}$ are respectively

$PQ$ is the ordinate of any point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1,$ if $QR$ is perpendicular to $A^{\text{'}}P,$ where $A{A}^{\text{'}}$ is transverse axis, then $\frac{AR}{RP}=$

The locus of mid-points of chords of $xy=c^2,$ of constant length $2a,$ is

$P, Q$ and $R$ are three points on the hyperbola $xy=c^2.$ If $PQ$ is parallel to the normal at $R,$ then the angle subtended by $PQ$ at $R$ is

If a circle having centre at the focus of the parabola $y^2=4ax$ touches the directrix of the parabola, then a point of intersection of the circle and the parabola may be

Equation of common tangent to parabola $y^2=40x$ and circle $x^2+y^2=50$ may be