KCET · Maths · Circle
The equation of two circles which touch the \(Y\)-axis at \((0,3)\) and make an intercept of 8 units on \(X\)-axis are
- A \(x^{2}+y^{2} \pm 10 x-6 y+9=0\)
- B \(x^{2}+y^{2} \pm 6 x-10 y+9=0\)
- C \(x^{2}+y^{2}-8 x \pm 10 y+9=0\)
- D \(x^{2}+y^{2}+10 x \pm 6 y+9=0\)
Answer & Solution
Correct Answer
(A) \(x^{2}+y^{2} \pm 10 x-6 y+9=0\)
Step-by-step Solution
Detailed explanation
Given, equation of circle touch the \(Y\)-axis at \((0,3)\).
So, from figure
\(
r=\sqrt{3^{2}+4^{2}}=5
\)The point \((0,3)\) and radius 5 satisfies the equation \(x^{2}+y^{2} \pm 10 x-6 y+9=0\)
Hence, it is the required equation of circle.
So, from figure
\(
r=\sqrt{3^{2}+4^{2}}=5
\)The point \((0,3)\) and radius 5 satisfies the equation \(x^{2}+y^{2} \pm 10 x-6 y+9=0\)
Hence, it is the required equation of circle.
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