Coordinate Geometry - Length of a Line Segment
Coordinate Geometry - Length of a Line Segment
A circle \(L\) is given by the equation \(4{{x}^{2}}+4{{y}^{2}}+8x-16y-29=0\).
- Find the coordinates of the centre of the circle and the radius of the circle.
- Determine, with working, if the point \(\left( -2,5 \right)\) lies inside or outside the circle.
Another circle \(M\), with centre \(\left( 4,14 \right)\), touches the circle \(L\) at one point. Find
- the distance between the two centres.
- all the possible equations of circle \(M\) in the form of \({{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\).
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Answer:(a) Centre \((-1,2)\), radius \(=\frac72\) (b) Inside circle \(L\) (c) \(13\text{ units}\) (d) \(x^2-8x+y^2-28y+\frac{487}{4}=0\) or \(x^2-8x+y^2-28y-\frac{241}{4}=0\)
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