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Theorem 3: Circle Through 3 Non-Collinear Points

A circle touc...

Question

A circle touches the line $L$ and the circle $C_{1}$ externally such that both the circles are on the same side of the line, then the locus of the center of the circle is?

A

ellipse

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B

hyperbola

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C

parabola

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D

parts of straight line

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Solution

The correct option is C parabola
From the given statement lets consider C be the center of the required circle.
draw a line parallel to L at a distance of r1
(C1-radius)from it.
Now $C P_{1} = A C \Rightarrow C$ lies on a parabola.

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