Conic Sections Question 496
Question: A circle touches the x-axis and also touches the circle with center (0,3) and radius 2, the locus of center of the circle is
Options:
A) A circle
B) An ellipse
C) A parabola
D) A hyperbola
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Let $ C_1(h,k) $ be the center of the circle. The circle touches the x-axis.
Then its radius is $ r_1=k $ Also, the circle touches the circle with center $ C_2(0,3) $ and radius $ r_2=2. $
Therefore, $ | C_1C_2 |=r_1+r_2 $ Or $ \sqrt{{{(h-0)}^{2}}+{{(k-3)}^{2}}}=| k+2 | $ Squaring. We get $ h^{2}-10k+5=0 $
Therefore, the locus is $ x^{2}-10y+5=0 $ , which is a parabola,
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