COMEDK · Maths · 12. Circle
What will be the equation of circle whose centre is \((1,2)\) and touches \(X\) - axis?
- A \(x^{2}+y^{2}-2 x-4 y+1=0\)
- B \(x^{2}-y^{2}+2 x+4 y+1=0\)
- C \(x^{2}+y^{2}+2 x-4 y-1=0\)
- D \(x^{2}+y^{2}+2 x+4 y-1=0\)
Answer & Solution
Correct Answer
(A) \(x^{2}+y^{2}-2 x-4 y+1=0\)
Step-by-step Solution
Detailed explanation
The centre of the circle is given as \((h, k) = (1, 2)\). Since the circle touches the X-axis, the radius \(r\) of the circle is equal to the absolute value of the y-coordinate of the centre. Thus, \(r = |k| = |2| = 2\). The standard equation of a circle with centre \((h, k)\)…
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