The equation of the normal at $(1, 1)$ to the circle $x^2 + y^2 - x - 3y - 4 = 0$ is

If $m_1, m_2$ are the slopes of the tangents drawn through the point $(-1, -2)$ to the circle $(x-3)^2 + (y-4)^2 = 4$,then $\sqrt{3}|m_1 - m_2| = $

The line $x + y = 2$ is tangent to the curve $x^2 = 3 - 2y$ at its point

If the line $x+3y=0$ is the tangent at $(0,0)$ to the circle of radius $1$,then the centre of one such circle is

For any two nonzero real numbers $a$ and $b$,if the line $\frac{x}{a} + \frac{y}{b} = 1$ is a tangent to the circle $x^2 + y^2 = 1$,then which of the following is true?

If $(3,-1)$ is one end of a diameter of the circle $x^2+y^2-2x+4y=0$,then the equation of the tangent at the other end of that diameter is