Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The centre of a circle passing through the point (0, 1) and touching the curve y = x 2 at (2, 4), is-
A
B
C
D
None
Text Solution
Verified by ExpertsThe correct answer is:
C
Equation of the tangent to the curve y = x 2 at (2, 4) is
= 2x
i.e. 4x – y – 4 = 0
Equation of any circle touching the curve y = x 2 at (2, 4) can be written as
(x – 2) 2 + (y – 4) 2 + λ (4x – y – 4) = 0
Since the circle passes through (0, 1), therefore
2 2 + 3 2 + λ (–1 – 4) = 0
Gives λ = 
Hence, equation the circle is
x 2 + y 2 + (4 λ – 4)x – ( λ + 8)y + 20 – 4 λ = 0
whose centre C ≡ 
≡ 
≡ 
.
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