TS EAMCET · Maths · Circle
If two circles \(x^2+y^2-6 x-6 y+13=0\) and \(x^2+y^2-8 y\) \(+9=0\) intersect at \(\mathrm{A}\) and \(\mathrm{B}\), then the focus of the parabola whose directrix is the line \(A B\) and vertex is the point \(O\) \((0,0)\) is
- A \(\left(\frac{3}{5}, \frac{1}{5}\right)\)
- B \(\left(-\frac{3}{5}, \frac{1}{5}\right)\)
- C \(\left(-\frac{3}{5}, -\frac{1}{5}\right)\)
- D \(\left(\frac{3}{5}, -\frac{1}{5}\right)\)
Answer & Solution
Correct Answer
(B) \(\left(-\frac{3}{5}, \frac{1}{5}\right)\)
Step-by-step Solution
Detailed explanation
\(C_1: x^2+y^2-6 x-6 y+13=0\) \(C_2: x^2+y^2-8 y+9=0\) Equation of common chord \(A B \equiv C_1-C_2=0\) \(\begin{aligned} & \therefore-6 x-6 y+13+8 y-9=0 \\ & \Rightarrow 6 x-2 y=4 \\ & \Rightarrow 3 x-y=2 \end{aligned}\) \(\therefore \quad\) Directrix is \(3 x-y-2=0 ... (i)\)…
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