The chord $ PQ $ of the rectangular hyperbola $xy = a^2$ meets the axis of $x$ at $A ; C $ is the mid point of $ PQ\ \& 'O' $ is the origin. Then the $ \Delta ACO$ is :
equilateral
isosceles
right angled
right isosceles.
A hyperbola having the transverse axis of length $\sqrt{2}$ has the same foci as that of the ellipse $3 x^{2}+4 y^{2}=12,$ then this hyperbola does not pass through which of the following points?
The curve $xy = c, (c > 0)$, and the circle $x^2 + y^2 = 1$ touch at two points. Then the distance between the points of contacts is
The equation of the tangent to the conic ${x^2} - {y^2} - 8x + 2y + 11 = 0$ at $(2, 1)$ is
The equation of common tangents to the parabola ${y^2} = 8x$ and hyperbola $3{x^2} - {y^2} = 3$, is
Area of the triangle formed by the lines $x -y = 0, x + y = 0$ and any tangent to the hyperbola $x^2 -y^2 = a^2$ is :-