The line $y+2x=5$ intersects the circle, ${{C}_{1}}$, ${{x}^{2}}+{{y}^{2}}-4x-6y=12$ at $A$

Question

The line $y+2x=5$ intersects the circle, ${{C}_{1}}$, ${{x}^{2}}+{{y}^{2}}-4x-6y=12$ at $A$ and $B$. State the centre of the circle and find the radius of the circle. Given that the coordinates of $A$ and $B$ are $\left( -1,7 \right)$ and $\left( \frac{17}{5},-\frac{9}{5} \right)$ respectively, show that $AB$ is not a diameter of the circle. Find the equation of the circle, ${{C}_{2}}$, when ${{C}_{1}}$ is reflected along the line $x=1$.

Accepted Answer

(a) Centre $(2,3)$, radius $5$ (b) $AB=\frac{22\sqrt5}{5}\ne10$, so $AB$ is not a diameter (c) $C_2:x^2+(y-3)^2=25$

Coordinate Geometry - Finding the Equation of a Circle

Coordinate Geometry - Finding the Equation of a Circle

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