A circle, ${{C}_{1}}$, has a diameter $AB$ where $A$ is the point $(6,-2)$ and $B$ is the

Question

A circle, ${{C}_{1}}$, has a diameter $AB$ where $A$ is the point $(6,-2)$ and $B$ is the point $\left( 12,6 \right)$. Find the coordinates of the centre and the radius of ${{C}_{1}}$. Find the equation of ${{C}_{1}}$. Show that the equation of the tangent to the circle at $A$ is $4y+3x=10.$

Accepted Answer

(a) Centre $=(9,2)$, radius $=5$ (b) $(x-9)^2+(y-2)^2=25$ (c) $4y+3x=10$

Coordinate Geometry - Tangents and Normals to Circles

Coordinate Geometry - Tangents and Normals to Circles

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