Coordinate Geometry - Tangents and Normals to Circles
Coordinate Geometry - Tangents and Normals to Circles
A circle \(C\) passes through the point \(P\left( 4,-3 \right)\) and has the same centre as the circle \({{x}^{2}}+{{y}^{2}}+4x-2y-1=0\).
- Find the equation of the circle \(C\).
- Find the equation of the tangent to the circle \(C\) at the point \(P\left( 4,-3 \right)\).
Another point \(Q\left( 4,q \right)\) which lies on the circle \(C\), is the same distance from the \(y\)-axis as the point \(P\).
- Find the coordinates of the point \(Q\) .
- Find the perimeter of the triangle \(POQ\), where \(O\) is the centre of the circle \(C\).
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Answer:(a) \((x+2)^2+(y-1)^2=52\) (b) \(y=\frac32x-9\) (c) \(Q=(4,5)\) (d) \(4\sqrt{13}+8\text{ units}\)
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