Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Minimum distance between the curves y 2 = x - 1 and x 2 = y - 1 is equal to
A
units
B
units
C
units
D
units
Text Solution
Verified by ExpertsThe correct answer is:
A
units
General point on the curve y 2 = x - 1 is 
and the general point on the curve x 2 = y - 1 is 
. Since both the curves are symmetrical about the line y = x, for the nearest point on the curve y 2 = x - 1 from the line y = x
Let, 
slopes of the tangents are same
...... (1)
Since PQ is perpendicular to line x =y
….(2)
Solving (1) & (2), we get 
therefore, PQ = 
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