Search any question & find its solution
Question:
Answered & Verified by Expert
If $x$ -axis is tangent to the circle $x^{2}+y^{2}+2 g x+2 f y+k=0$, then which one of the following is correct?
Options:
Solution:
1451 Upvotes
Verified Answer
The correct answer is:
$g^{2}=k$
Length of intercept on the $x$ -axis made by the circle
$$
x^{2}+y^{2}+2 g x+2 f y+k=0 \text { is } 2 \sqrt{g^{2}-k}
$$
Since, circle touches the $\mathrm{x}$ -axis therefore intercept on $\mathrm{x}=$ axis $=0$
$$
\begin{array}{l}
\therefore \quad \sqrt{g^{2}-k}=0 \\
\Rightarrow \quad g^{2}=k
\end{array}
$$
$$
x^{2}+y^{2}+2 g x+2 f y+k=0 \text { is } 2 \sqrt{g^{2}-k}
$$
Since, circle touches the $\mathrm{x}$ -axis therefore intercept on $\mathrm{x}=$ axis $=0$
$$
\begin{array}{l}
\therefore \quad \sqrt{g^{2}-k}=0 \\
\Rightarrow \quad g^{2}=k
\end{array}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.