Circle And System Of Circles Question 160
Question: The equation of the circle with centre on x-axis, radius 5 and passing through the point (2, 3), is
Options:
A) $ x^{2}+y^{2}+4x-21=0 $
B) $ x^{2}+y^{2}+4x+21=0 $
C) $ x^{2}+y^{2}-4x-21=0 $
D) $ x^{2}+y^{2}+5x-21=0 $
Show Answer
Answer:
Correct Answer: A
Solution:
Let centre be $ (-g,\ 0) $ , then $ \sqrt{g^{2}-c}=5\Rightarrow c=g^{2}-25 $
Also it passes through (2, 3), therefore $ 13+4g+g^{2}-25=0\Rightarrow g=-6,\ 2 $
Hence the equations are $ x^{2}+y^{2}-12x+11=0 $ and $ x^{2}+y^{2}+4x-21=0 $ .
BETA
