If a circle is such that it touches the line and the circle externally, such that both the circles are on the same side of the line, then the locus of centre of the circle is [2006]

Question

$A B C D$ is a square of side length 2 units. $C_{1}$ is the circle touching all the sides of the square $A B C D$ and $C_{2}$ is the circumcircle of square $A B C D$ . $L$ is a fixed line in the same plane. [2006]

Q. If a circle is such that it 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 centre of the circle is

Smart Achievers · Accepted Answer

(3)

Let $C'$ be the said circle touching $C_{1}$ and $L$ , so that $C_{1}$ and $C'$ are on the same side of $L$ . Let us draw a line $T$ parallel to $L$ at a distance equal to the radius of circle $C_{1},$ on the opposite side of $L$ .

Then the centre of $C'$ is equidistant from the centre of $C_{1}$ and from line $T$ .

$\Rightarrow$ Locus of centre of $C'$ is a parabola.

Solution

1 ellipse

2 hyperbola

3 parabola

4 pair of straight line

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