A circle $C$ is given by the equation $3x^2 + 3y^2 + 9x - 15y - 39 = 0$. Find the coordinates of

Question

A circle $C$ is given by the equation $3x^2 + 3y^2 + 9x - 15y - 39 = 0$. Find the coordinates of the centre of the circle and the radius of the circle. Determine, with working, if the point $(-3, 5)$ lies inside or outside the circle. Another circle $M$, with centre $\left( \frac{\sqrt{123} - 3}{2}, 12 \right)$, touches the circle $C$ at one point. Find the distance between the two centres. all possible equations of $M$ in the form $x^2 + y^2 + 2gx + 2fy + c = 0$.

Accepted Answer

(a) Centre $\left(-\frac32,\frac52\right)$, radius $\sqrt{\dfrac{43}{2}}$. (b) Inside. (c) $11$. (d) $x^2+y^2+(3-\sqrt{123})x-24y+\frac{69-3\sqrt{123}}2\pm11\sqrt{86}=0$.

Coordinate Geometry - Finding the Centre and Radius of a Circle

Coordinate Geometry - Finding the Centre and Radius of a Circle

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