EXERCISE 13.6

The equation of the hyperbola whose asymptotes are the straight lines $3x-4y+7=0$ and $4x+3y+1=0$ and which passes through the origin, is

If the line $ax+by+c=0$ is a normal to the curve $xy=2,$ then

The asymptotes of $xy=hx+ky$ are

If $PN$ is the perpendicular from a point on a rectangular hyperbola to its asymptotes, the locus of the mid-point of $PN$ is

The point of intersection of tangents at $t_1$ and $t_2$ to the hyperbola $xy=c^2$ is

A rectangular hyperbola whose centre is $C$ is cut by any circle of radius $r$ in four points $P, Q, R, S.$ The value of $C{P}^2+C{Q}^2+C{R}^2+C{S}^2$ is equal to

The equation to the chord joining two points $\left(x_1, y_1\right)$ and $\left(x_2, y_2\right)$ on the rectangular hyperbola $xy=c^2$ is

The equation of the common tangent to the curves $y^2=8x$ and $xy=-1,$ is