MHT CET · Maths · Circle
The equation of the circle, concentric with the circle \(x^2+y^2-6 x-4 y-12=0\) and touching the X -axis is
- A \(x^2+y^2-6 x-4 y+5=0\)
- B \(x^2+y^2-6 x-4 y+17=0\)
- C \(x^2+y^2-6 x-4 y+9=0\)
- D \(x^2+y^2-6 x-4 y+4=0\)
Answer & Solution
Correct Answer
(C) \(x^2+y^2-6 x-4 y+9=0\)
Step-by-step Solution
Detailed explanation
Centre of the circle
\(x^2+y^2-6 x-4 y-12=0 \text { is } \mathrm{C}(3,2)\)
Since it touches X-axis, \(\mathrm{r}=2\)
Hence, the required equation of the circle is
\(\begin{aligned}
& (x-3)^2+(y-2)^2=2^2 \\
& \Rightarrow x^2+y^2-6 x-4 y+9=0
\end{aligned}\)
\(x^2+y^2-6 x-4 y-12=0 \text { is } \mathrm{C}(3,2)\)
Since it touches X-axis, \(\mathrm{r}=2\)
Hence, the required equation of the circle is
\(\begin{aligned}
& (x-3)^2+(y-2)^2=2^2 \\
& \Rightarrow x^2+y^2-6 x-4 y+9=0
\end{aligned}\)
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