The slope of the tangent at the point $(h,h)$ of the circle ${x^2} + {y^2} = {a^2}$ is

The number of tangents that can be drawn from $(0, 0)$ to the circle ${x^2} + {y^2} + 2x + 6y – 15 = 0$ is

Let $O$ be the centre of the circle $x ^2+ y ^2= r ^2$, where $r >\frac{\sqrt{5}}{2}$. Suppose $P Q$ is a chord of this circle and the equation of the line passing through $P$ and $Q$ is $2 x+4 y=5$. If the centre of the circumcircle of the triangle $O P Q$ lies on the line $x+2 y=4$, then the value of $r$ is. . . .

If the line $3x – 4y = \lambda $ touches the circle ${x^2} + {y^2} – 4x – 8y – 5 = 0$, then $\lambda $ is equal to

If the line $y = mx + c$be a tangent to the circle ${x^2} + {y^2} = {a^2}$, then the point of contact is