Circle And System Of Circles Question 178
Question: Circles are drawn through the point (2, 0) to cut intercept of length 5 units on the x-axis. If their centres lie in the first quadrant, then their equation is
Options:
A) $ x^{2}+y^{2}+9x+2fy+14=0 $
B) $ 3x^{2}+3y^{2}+27x-2fy+42=0 $
C) $ x^{2}+y^{2}-9x+2fy+14=0 $
D) $ x^{2}+y^{2}-2fy-9y+14=0 $
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Answer:
Correct Answer: C
Solution:
The circle g, f, c passes through (2, 0)
$ \therefore $ $ 4+4g+c=0 $ ………….(i)
Intercept on x-axis is $ 2\sqrt{(g^{2}-c)}=5 $
$ \therefore \ 4(g^{2}+4g+4)=25 $ by (i) or $ (2g+9)(2g-1)=0\Rightarrow g=-\frac{9}{2},\ \frac{1}{2} $
Since centre $ (-g,\ -f) $ lies in 1st quadrant, we choose $ g=-\frac{9}{2} $ so that $ -g=\frac{9}{2} $ (positive).
$ \therefore \ c=14 $ , (from (i)).
BETA
