A circle is drawn with $y- $ axis as a tangent and its centre at the point which is the reflection of $(3, 4)$ in the line $y = x$. The equation of the circle is
$x^2 + y^2 - 6x - 8y + 16 = 0$
$x^2 + y^2 - 8x - 6y + 16 = 0$
$x^2 + y^2 - 8x - 6y + 9 = 0$
$x^2 + y^2 - 6x - 8y + 9 = 0$
Lines are drawn from a point $P (-1, 3)$ to a circle $x^2 + y^2 - 2x + 4y - 8 = 0$. Which meets the circle at $2$ points $A$ & $B$, then the minimum value of $PA + PB$ is
If the straight line $4x + 3y + \lambda = 0$ touches the circle $2({x^2} + {y^2}) = 5$, then $\lambda $ is
Given the circles ${x^2} + {y^2} - 4x - 5 = 0$and ${x^2} + {y^2} + 6x - 2y + 6 = 0$. Let $P$ be a point $(\alpha ,\beta )$such that the tangents from P to both the circles are equal, then
The equation of the normal at the point $(4,-1)$ of the circle $x^2+y^2-40 x+10 y=153$ is
The equations of the tangents to circle $5{x^2} + 5{y^2} = 1$, parallel to line $3x + 4y = 1$ are