Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The set of points on the axis of the parabola y 2 - 2y - 4x + 5 = 0 from which all the three normals drawn to the parabola are real and distinct, is
A
{(x, 1) : x >3}
B
{(x, -1) : x > 1}
C
{(x,3):x 
1}
1}
D
{(x, -3) : x 
3}
3}
Text Solution
Verified by ExpertsThe correct answer is:
A
{(x, 1) : x>3}
Given equation of the parabola can be rewritten as
Axis of the parabola is y = 1,
equation of normal is
(y - 1) = m (x - 1) -2m - m 3
Let (h, 1) is a point on its axis, then
0 = m (h - 1) - 2m - m 3
m 2 = h - 3
h> 3 for real & distinct values of m
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