Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The equation of the parabola whose focus is the point (0, 0) and the tangent at the vertex is 
is
A
B
C
D
Text Solution
Verified by ExpertsThe correct answer is:
C
Let focus is 
and A is the vertex of parabola. Take any point Z such that AS = AZ. Given tangent at vertex is 
Since directrix is parallel to the tangent at the vertex.
Equation of directrix is 
, where 
is constant.
A is midpoint of SZ , 
SZ = 2. SA
⇒ ⇒ 
⇒ ⇒ 
i.e. 
Directrix in this case always lies in II nd quadrant
∴ ∴ 
Hence equation of directrix is 
Now, P be any point on parabola
∴ ∴ SP = PM ⇒ ⇒ 
⇒ ⇒ 
⇒ ⇒ 
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