AP EAMCET · Maths · Circle
Let the circle \(S \equiv x^2+y^2+2 g x+2 f y+c=0\) cut the circles \(x^2+y^2-2 x+2 y-2=0\) and \(x^2+y^2+4 x-6 y+9=0\) orthogonally. If the centre of the circle \(S=0\) lies on the line \(2 \mathrm{x}+3 \mathrm{y}-2=0\), then \(2 \mathrm{~g}+\mathrm{f}=\)
- A \(\mathrm{c}\)
- B \(c+f\)
- C \(2 \mathrm{~g}-\mathrm{c}\)
- D \(c-f\)
Answer & Solution
Correct Answer
(D) \(c-f\)
Step-by-step Solution
Detailed explanation
In circle \(S=x^2+y^2+2 g x+2 f y+c=0...(1)\) centre \(=(-g,-f), g_{\hat{i}}=g, f_1=f, c_1=c\) In circle \(x^2+y^2-2 x+2 y-2=0...(2)\) \[ g_2=-1, f_2=1, c_2=-2 \] In circle \(x^2+y^2+4 x-6 y+9=0...(3)\) \[ g_3=2, f_3=-3, c_3=9 \] Since eq (1) \& (2) are orthogonal hence…
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