AP EAMCET · Maths · Circle
The equation of the circle with centre \((2,3)\) and touching the line \(3 x-4 y+1=0\) is
- A \(x^2+y^2+4 x+4 y+12=0\)
- B \(x^2+y^2-4 x-6 y-14=0\)
- C \(x^2+y^2-4 x-6 y+14=0\)
- D \(x^2+y^2-4 x-6 y+12=0\)
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…
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