If a triangle $ABC$ has vertices $A(1,-6), B(2,-3)$ and $C(3,-2)$, then the coordinates of its orthocenter are....

If $\theta$ is the acute angle between the lines represented by the equation $x^2 - 3xy + 2y^2 = 0$, then $\dfrac{3\sin\theta + 2\cos\theta}{3\sin\theta - 2\cos\theta} = $

The triangle formed by the lines $2x^2 - 3xy - 2y^2 = 0$ and $3x - y = 7$ is...

The centre and radius of the circle $(a+1)x^2 + 3y^2 - 6x + 9y + a + 4 = 0$ are respectively ...