28. A circle touches the line L and the circle $\mathrm { C } _ { 1 }$ externally such that both the circles are on the same side of the line, then the locus of centre of the circle is (A) ellipse (B) hyperbola (C) parabola (D) parts of straight line Sol. (C) Let C be the centre of the required circle. Now draw a line parallel to L at a distance of $\mathrm { r } _ { 1 }$ (radius of $\mathrm { C } _ { 1 }$ ) from it. Now $\mathrm { CP } _ { 1 } = \mathrm { AC } \Rightarrow \mathrm { C }$ lies on a parabola. [Figure]
A circle touches the line L and the circle $\mathrm { C } _ { 1 }$ externally such that both the circles are on the same side of the line, then the locus of centre of the circle is
28. A circle touches the line L and the circle $\mathrm { C } _ { 1 }$ externally such that both the circles are on the same side of the line, then the locus of centre of the circle is\\
(A) ellipse\\
(B) hyperbola\\
(C) parabola\\
(D) parts of straight line
Sol. (C)\\
Let C be the centre of the required circle.\\
Now draw a line parallel to L at a distance of $\mathrm { r } _ { 1 }$ (radius of $\mathrm { C } _ { 1 }$ ) from it.\\
Now $\mathrm { CP } _ { 1 } = \mathrm { AC } \Rightarrow \mathrm { C }$ lies on a parabola.\\
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