Question

The equation of line parallel to the tangent to the circle $ {{x}^{2}}+{{y}^{2}}={{r}^{2}} $ at the point $ ({{x}_{1}},{{y}_{1}}) $ and passing through origin, is:

• A. $ x{{y}_{1}}+{{x}_{1}}y=0 $
• B. $ x{{x}_{1}}-y{{y}_{1}}=0 $
• C. $ x{{x}_{1}}+y{{y}_{1}}=0 $
• D. $ xy-{{x}_{1}}y=0 $

Answer 1

Answer: (C)

As we know that tangent on point $\left(x_{1}, y_{1}\right)$ of
the circle $x^{2}+y^{2}=r^{2}$ is $x x_{1}+y y_{1}=r^{2} \ldots$ (i)
The required line is parallel to the tangent line
i.e., $x x_{1}+y y_{1}=k$
Since, it is passing through origin.
$\Rightarrow k=0$
$\therefore x x_{1}+y y_{1}=0$