AP EAMCET · Maths · Circle
The circumference of a circle passing through the point \((4,6)\) with two normals represented by \(2 x-3 y+4=0\) and \(x+y-3=0\) is
- A \(5 \pi\)
- B \(10 \pi\)
- C \(25 \pi\)
- D \(8 \pi\)
Answer & Solution
Correct Answer
(B) \(10 \pi\)
Step-by-step Solution
Detailed explanation
Intersection of two normals will be the centre of the circle. \(2 x-3 y+4=0\)....(i) and \(x+y-3=0\) ....(ii) Solving equations (i) and (ii) we get, Centre \(=(1,2)\) Also, circle passes through \((4,6)\) \(\therefore\) Radius \((r)=\sqrt{(4-1)^2+(6-2)^2}=5\) So, circumference…
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