TS EAMCET · Maths · Circle
A circle C touches X -axis and makes an intercept of length 2 units on Y -axis. If the centre of this circle lies on the line \(y=x+1\) then a circle passing through the centre of the circle C is
- A \(x^2+y^2-2 x-4 y+1=0\)
- B \(x^2+y^2-26 x-20 y+19=0\)
- C \(x^2+y^2-20 x-26 y+19=0\)
- D \(x^2+y^2+2 x-4 y+1=0\)
Answer & Solution
Correct Answer
(B) \(x^2+y^2-26 x-20 y+19=0\)
Step-by-step Solution
Detailed explanation
Let the centre of circle C be \((h,k)\) and radius be \(r\). Touches X-axis \(\implies r = |k|\). Y-intercept length is 2 \(\implies 2\sqrt{r^2-h^2}=2 \implies r^2-h^2=1\). Centre lies on \(y=x+1 \implies k=h+1\). \(k^2-h^2=1\).…
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