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The centre of the circle passing through the point (0, 1) and touching the curve y = x2 at (2, 4) is (1983 - 1 Mark)
  • a)
  • b)
  • c)
  • d)
    none of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The centre of the circle passing through the point (0, 1) and touching...
Let C (h, k) be the centre of circle touching x2 = y at B (2, 4). Then equation of common tangent at B is
i.e., 4x – y = 4
Radius is perpendicular to this tangent
 = -1 ⇒ 4k = 18… (1)        
Also AC = BC ⇒ h2 + (k – 1)2 = (h – 2)2 + (k – 4)2
⇒ 4h + 6k = 19 … (2)
Solving (1) and (2) we get the centre as  
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