AP EAMCET · Maths · Circle
If a circle touches the lines \(3 x-4 y-10=0\) and \(3 x-4 y+30=0\) and its centre lies on the line \(x+2 y=0\), then the equation of the circle is
- A \(x^2+y^2+4 x-2 y-11=0\)
- B \(x^2+y^2+2 x-4 y-11=0\)
- C \(x^2+y^2-4 x+2 y-11=0\)
- D \(x^2+y^2+2 x-y-11=0\)
Answer & Solution
Correct Answer
(A) \(x^2+y^2+4 x-2 y-11=0\)
Step-by-step Solution
Detailed explanation
Distance between parallel lines \(3 x-4 y-10=0\) and \(3 x-4 y+30=0\) is the length of diametre of required circle, so radius \[ =\frac{1}{2} \frac{40}{\sqrt{9+16}}=4 \] and mid-point of intersection of lines \(3 x-4 y-10=0, x+2 y=0\) and \(3 x-4 y+30=0\), \(x+2 y=0\), is the…
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