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 ...

If the line $4x + 3y = 7$ touches the hyperbola $x^2 - y^2 = 7$, then the sum of the co-ordinates of the point of contact is...

If $\lim\limits_{x \to 0} \dfrac{(4^x - 1)^3}{\tan\left(\dfrac{x}{4}\right)\log\left(1 + \dfrac{x^2}{3}\right)} = 96(\log a)^b$, then $(a + b) = $