KCET · Maths · Vector Algebra
Equation of circle with center \( (-a,-b) \) and radius \( \sqrt{a^{2}-b^{2}} \) is
- A \( x^{2}+y^{2}-2 a x-2 b y-2 b^{2}=0 \)
- B \( x^{2}+y^{2}-2 a x+2 b y+2 a^{2}=0 \)
- C \( x^{2}+y^{2}+2 a x+2 b y+2 b^{2}=0 \)
- D \( x^{2}+y^{2}-2 a x-2 b y+2 b^{2}=0 \)
Answer & Solution
Correct Answer
(C) \( x^{2}+y^{2}+2 a x+2 b y+2 b^{2}=0 \)
Step-by-step Solution
Detailed explanation
Given that, center is \((-a,-b)\) and radius is \(\sqrt{a^{2}-b^{2}}\)
Thus, equation of circle is
\((x+a)^{2}+(y+b)^{2}=\left(\sqrt{a^{2}-b^{2}}\right)^{2}\)
\(\Rightarrow x^{2}+y^{2}+2 a x+2 b y+2 b^{2}=0\)
Thus, equation of circle is
\((x+a)^{2}+(y+b)^{2}=\left(\sqrt{a^{2}-b^{2}}\right)^{2}\)
\(\Rightarrow x^{2}+y^{2}+2 a x+2 b y+2 b^{2}=0\)
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