AP EAMCET · Maths · Circle
The equation of the circle with \((1,1)\) as centre and which cuts a chord of length \(4 \sqrt{2}\) units on the line \(x+y+1=0\) is
- A \(x^2+y^2-2 x-2 y-21=0\)
- B \(2 x^2+2 y^2-4 x-4 y-21=0\)
- C \(x^2+y^2-2 x-2 y-10=0\)
- D \(2 x^2+2 y^2-4 x-4 y-25=0\)
Answer & Solution
Correct Answer
(B) \(2 x^2+2 y^2-4 x-4 y-21=0\)
Step-by-step Solution
Detailed explanation
\(d = \frac{|1(1)+1(1)+1|}{\sqrt{1^2+1^2}} = \frac{3}{\sqrt{2}}\) \(l = \frac{4\sqrt{2}}{2} = 2\sqrt{2}\) \(r^2 = d^2 + l^2 = \left(\frac{3}{\sqrt{2}}\right)^2 + (2\sqrt{2})^2 = \frac{9}{2} + 8 = \frac{25}{2}\) \((x-1)^2 + (y-1)^2 = \frac{25}{2}\)…
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