JEE Main 2017 — Coordinate Geometry

If a point $P(0,-2)$ and $Q$ is any point on the circle, ${x}^{2}+{y}^{2}-5x-y+5=0$, then the maximum value of ${(PQ)}^{2}$ is

If two parallel chords of a circle, having diameter $4$ units, lie on the opposite sides of the center and subtend angles ${\mathrm{cos}}^{-1}⁡(\frac{1}{7})$ and ${\mathrm{sec}}^{-1}⁡(7)$ at the center respectively, then the distance between these chords is:

Let $k$ be an integer such that the triangle with vertices $(k,-3k), (5,k)$ and $(-k, 2)$ has area $28$ sq. units. Then the orthocenter of this triangle is at the point:

The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points $(4,-1)$ and $(-2,2)$ is

The eccentricity of an ellipse whose centre is at the origin is $\frac{1}{2}$ . If one of its directrices is $x=-4$ , then the equation of the normal to it at $(1,\frac{3}{2})$ is:

The locus of the point of intersection of the straight lines, $tx-2y-3t=0$ and $x-2ty+3=0 (t\in R),$ is:

The radius of a circle, having minimum area, which touches the curve $y=4-{x}^{2}$ and the lines, $y=|x|$ is: