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CGP EDU Academic Team
Published on: August 14, 2026
The sum of the ordinates of point of contacts of the common tangent to the parabolas y = x 2 + 4x + 8 and y = x 2 + 8x + 4, is
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Any point on y = x 2 + 4x + 8 is P(h,h 2 + 4h + 8).
= 2h + 4
Tangent at P is (2h + 4) x – y = h 2 – 8.
It is sufficient to have only one solution for equations y = x 2 + 8x + 4, y = (2h + 4) x + 8 – h 2
⇒ x 2 + (4 – 2h) x + h 2 – 4 = 0
⇒ D = 0
(4 – 2h) 2 – 4(h 2 – 4) = 0
⇒ h = 2
8x – y + 4 = 0
coordinates of point of contact are (2, 20) and (0, 4)
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