Circle And System Of Circles Question 3
Question: The locus of the point of intersection of the tangents at the extremities of a chord of the circle $ x^{2}+y^{2}=a^{2} $ which touches the circle $ x^{2}+y^{2}=2ax $ is
Options:
A) $ y^{2}=a(a-2x) $
B) $ x^{2}=a(a-2y) $
C) $ x^{2}+y^{2}={{(y-a)}^{2}} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ T\equiv hx+ky-a^{2}=0 $
$ \Rightarrow a=\frac{ah-a^{2}}{\sqrt{h^{2}+k^{2}}} $
$ P(3,,4) $ .
therefore $ k^{2}=a(a-2h) $ \ The locus is $ y^{2}=a(a-2x) $ .
BETA
