Circle And System Of Circles Question 13
Question: Equation of the pair of tangents drawn from the origin to the circle $ x^{2}+y^{2}+2gx+2fy+c=0 $ is
Options:
A) $ gx+fy+c(x^{2}+y^{2}) $
B) $ {{(gx+fy)}^{2}}=x^{2}+y^{2} $
C) $ {{(gx+fy)}^{2}}=c^{2}(x^{2}+y^{2}) $
D) $ {{(gx+fy)}^{2}}=c(x^{2}+y^{2}) $
Show Answer
Answer:
Correct Answer: D
Solution:
Equation of pair of tangents is $ SS_1=T^{2} $ , where $ T=xx_1+yy_1+g(x+x_1)+f(y+y_1)+c $
$ \Rightarrow c(x^{2}+y^{2}+2gx+2fy+c)={{(gx+fy+c)}^{2}} $
$ \Rightarrow c(x^{2}+y^{2})={{(gx+fy)}^{2}} $ .
BETA
