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AP EAMCET · Maths · Circle

The equation of the circle with centre \((2,3)\) and touching the line \(3 x-4 y+1=0\) is

  1. A \(x^2+y^2+4 x+4 y+12=0\)
  2. B \(x^2+y^2-4 x-6 y-14=0\)
  3. C \(x^2+y^2-4 x-6 y+14=0\)
  4. D \(x^2+y^2-4 x-6 y+12=0\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(x^2+y^2-4 x-6 y+12=0\)

Step-by-step Solution

Detailed explanation

Centre \(c=(2,3)\) radius \(=\) Perpendicular distance from centre \((2,3)\) to the line \(3 x-4 y+1=0\) \(\begin{aligned} & r=\frac{|3(2)-4(3)+1|}{\sqrt{3^2+(-4)^2}}=\frac{|7-12|}{\sqrt{25}} \\ & r=\frac{5}{5}=1 \end{aligned}\) Equation of circle is…