If $A(2, -3)$ and $C(-6, 7)$ are opposite vertices of a rhombus ABCD, then the equation of diagonal BD is

The measure of the acute angle between the pair of lines $2x^2 + xy - y^2 - x + 2y - 1 = 0$ is:

The joint equation of a pair of lines passing through point $(1,4)$, one of which is parallel to X-axis and the other makes an angle of $45^\circ$ with the positive direction of X-axis, is

If a circle passes through the points $(2,3)$ and $(4,5)$ and its center lies on the straight line $y - 4x + 3 = 0$, then its equation is......