COMEDK · Maths · 12. Circle
The equation of the circle which touches the \(x\)-axis, passes through the point \((1,1)\) and whose centre lies on the line \(x+y=3\) in the first quadrant is
- A \(x^2+y^2+4 x+2 y+4=0\)
- B \(x^2+y^2-4 x-2 y+4=0\)
- C \(x^2+y^2+4 x-2 y+4=0\)
- D \(x^2+y^2-4 x+2 y+4=0\)
Answer & Solution
Correct Answer
(B) \(x^2+y^2-4 x-2 y+4=0\)
Step-by-step Solution
Detailed explanation
Let the centre of the circle be \((h, k)\). Since the circle touches the \(x\)-axis, the radius \(r\) is equal to \(|k|\). As the circle is in the first quadrant, \(k > 0\), so \(r = k\). The centre \((h, k)\) lies on the line \(x + y = 3\), so \(h + k = 3\), which implies…
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