What is the area of the quadrilateral formed by the line $|x| + |y| = 1$?

At what angle do the curves $x^2 - y^2 = 5$ and $\frac{x^2}{18} + \frac{y^2}{8} = 1$ intersect at any common point?

$A$ circle is described whose centre is the vertex and whose diameter is three-quarters of the latus rectum of the parabola $y^2 = 4ax$. If $PQ$ is the common chord of the circle and the parabola and $L_1L_2$ is the latus rectum,then the area of the trapezium $PL_1L_2Q$ is:

Let $P$ be the point of intersection of the common tangents to the parabola $y^2 = 12x$ and the hyperbola $8x^2 - y^2 = 8$. If $S$ and $S'$ denote the foci of the hyperbola where $S$ lies on the positive $x$-axis,then $P$ divides $SS'$ in the ratio:

The circle $x^2 + y^2 = 5$ meets the parabola $y^2 = 4x$ at $P$ and $Q$. Then the length $PQ$ is equal to:

If the ellipse $4x^2 + 9y^2 = 36$ is confocal with a hyperbola whose length of the transverse axis is $2$,then the points of intersection of the ellipse and hyperbola lie on the circle: