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CGP EDU Academic Team
Published on: August 13, 2026
The common tangents to the circle x 2 + y 2 = a 2 /2 and the parabola y 2 = 4ax intersect at the focus of the parabola-
Text Solution
Verified by ExpertsThe correct answer is:
C
Equation of a tangent to the parabola y 2 = 4ax is y = mx + a/m.
⇒ 2 = m 2 (1 + m 2 )
⇒ m 4 + m 2 – 2 = 0 ⇒ (m 2 – 1) (m 2 + 2) = 0
⇒ m 2 = 1 ⇒ x = ± 1
Hence the common tangents are y = x + a and y = –x –a which intersect at the point
(–a, 0) which is the focus of the parabola y 2 = –4ax.
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