If the eccentricities of two conics $S$ and $S'$ are $e$ and $e'$ respectively,such that $e^2 + e'^2 = 3$,then both $S$ and $S'$ are:

If the circle $x^2+y^2=a^2$ intersects the hyperbola $xy=c^2$ in four points $(x_i, y_i)$,for $i=1, 2, 3, 4$,then $y_1+y_2+y_3+y_4$ equals

If the tangent and normal to a rectangular hyperbola $xy = c^2$ at a variable point cut off intercepts $a_1, a_2$ on the $x$-axis and $b_1, b_2$ on the $y$-axis,then $(a_1a_2 + b_1b_2)$ is

The equations of the transverse and conjugate axes of the hyperbola $16x^2 - y^2 + 64x + 4y + 44 = 0$ are

$A$ hyperbola passes through the point $P(\sqrt{2}, \sqrt{3})$ and has foci at $(\pm 2, 0)$. Then the tangent to this hyperbola at $P$ also passes through the point:

The equation of the normal to the curve $3x^2 - y^2 = 8$,which is parallel to the line $x + 3y = 10$,is