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AP EAMCET · Maths · Circle

A circle is drawn touching the \(X\)-axis, with its centre at the point of reflection of \((m, n)\) on the line \(y-x=0\). Then the equation of the circle is

  1. A \(x^2+y^2-2 m x-2 n y+m^2=0\)
  2. B \(x^2+y^2-2 m x+2 n y+m^2=0\)
  3. C \(x^2+y^2+2 n x-2 m y-n^2=0\)
  4. D \(x^2+y^2-2 n x-2 m y+n^2=0\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(x^2+y^2-2 n x-2 m y+n^2=0\)

Step-by-step Solution

Detailed explanation

The point of reflection of \((m, n)\) on the line \(y-x=0\) is \((n, m)\), so equation of circle having centre \((n, m)\) and let radius \(r\) is \((x-n)^2+(y-m)^2=r^2\)...(i) \(\because\) Circle (i) touches the \(X\)-axis, so \(r=m\) So, equation of required circle is…