Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
If the circle $x^{2}+y^{2}+2 g x+2 f y+c=0(c>0)$ touches the $y$ axis, then which one of the following is correct?
MathematicsCircleNDANDA 2008 (Phase 1)
Options:
  • A $\mathrm{g}=-\sqrt{\mathrm{c}}$ only
  • B $\mathrm{g}=\pm \sqrt{\mathrm{c}}$
  • C $\mathrm{f}=\sqrt{\mathrm{c}}$ only
  • D $\mathrm{f}=\pm \sqrt{\mathrm{c}}$
Solution:
2934 Upvotes Verified Answer
The correct answer is: $\mathrm{f}=\pm \sqrt{\mathrm{c}}$
As given, the circle $x^{2}+y^{2}+2 g x+2 f y+c=0$ touches y-axis. then $\mathrm{r}=\pm \mathrm{g}$ and $\mathrm{g}^{2}+\mathrm{f}^{2}-\mathrm{c}=\mathrm{g}^{2}$
$\Rightarrow \mathrm{f}^{2}-\mathrm{c}=0 \Rightarrow \mathrm{f}^{2}=\mathrm{c} \Rightarrow \mathrm{f}=\pm \sqrt{\mathrm{c}}$

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.