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Let $A B C D$ be a square of side length 2 units. $C_2$ is the circle through vertices $A, B, C, D$ and $C_1$ is the circle touching all the sides of square $A B C D$. $L$ is the line through $A$.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 centre of the circle is
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Read the following passage and answer the questions.
Let $A B C D$ be a square of side length 2 units. $C_2$ is the circle through vertices $A, B, C, D$ and $C_1$ is the circle touching all the sides of square $A B C D$. $L$ is the line through $A$.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 centre of the circle is
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The correct answer is:
parabola
parabola
Let $C$ be the centre of the required circle.
Now, draw a line parallel to $L$ at a distance of $r_1$ (radius of $C_1$ ) from it. Now, $C P_1=A C$
$\Rightarrow C$ lies on a parabola.
Now, draw a line parallel to $L$ at a distance of $r_1$ (radius of $C_1$ ) from it. Now, $C P_1=A C$
$\Rightarrow C$ lies on a parabola.
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