Published by:
CGP EDU Academic Team
Published on: August 13, 2026
A circle (x – α ) 2 + (y – β ) 2 = 8 is inscribed in a parabola
y 2 = 4x. Find [ α + β ] where [x] represents greatest integer ≤ x.
Text Solution
Verified by ExpertsThe correct answer is:
0003
Ans. 0003
Sol.
By symmetry, circle must be centred on x axis.
so β = 0
Now, normal to y 2 = 4x at p(m 2 , –2m) is
y = mx – 2m – m 3 ( α , 0) must lie on it ⇒ m( α – 2) – m
2 = 0
m 2 = α –2
Now, (m 2 – α ) 2 + 4m 2 = 8
so ( α – 2 – α ) 2 + 4( α – 2) = 8
⇒ α = 3
So α + β = 3 + 0
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
If a double ordinate of the parabola be of length , then the angle between the lines joining the …
PQ is a double ordinate of the parabola . The locus of the points of trisection of PQ is
If the vertex of a parabola be at origin and directrix be , then its latus rectum is
The latus rectum of a parabola whose directrix is and focus is (3, – 4), is
The points on the parabola whose ordinate is three times the abscissa are
The points on the parabola whose focal distance is 4, are