JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
The locus of the centres of the circles, which touch the circle, \(x^2 + y^2 = 1\) externally, also touch the \(y-\) axis and lie in the first quadrant is
- A \(x\, = \,\sqrt {1\, + \,2y\,} ,\,y\, \ge \,0\)
- B \(x\, = \,\sqrt {1\, + \,4x\,} ,\,x\, \ge \,0\)
- C \(x\, = \,\sqrt {1\, + \,4y\,} ,\,y\, \ge \,0\)
- D \(x\, = \,\sqrt {1\, + \,2x\,} ,\,x\, \ge \,0\)
Answer & Solution
Correct Answer
(D) \(x\, = \,\sqrt {1\, + \,2x\,} ,\,x\, \ge \,0\)
Step-by-step Solution
Detailed explanation
\(\sqrt {{h^2} + {k^2}} = \left| h \right| + 1\) \( \Rightarrow {x^2} + {y^2} = {x^2} + 1 + 2x\) \( \Rightarrow {y^2} = 1 + 2x\) \( \Rightarrow y = \sqrt {1 + 2x} ;x \ge 0\)
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