Equation of Family of Circles Touching a Line and Passing through a Given Point on the Line
The circle pa...
Question
The circle passing through (1,−2) and touching the x-axis at (3,0) also passes through the point
A
(−2,−2)
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B
(2,−5)
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C
(5,−2)
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D
(−2,5)
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Solution
The correct option is C(5,−2)
As the circle is touching the x−axis at (3,0),
let the centre of the circle be C(3,k)
Radius, r=|k|
Equation of the circle is (x−3)2+(y−k)2=k2
Above circle passes through (1,−2).
Then, (1−3)2+(−2−k)2=k2 ⇒k=−2
Hence, equation of the circle is (x−3)2+(y+2)2=4
Clearly, (5,−2) satisfies it.