JEE Main 2019 — Hyperbola Question with Solution
From: JEE Main 2019 (Online) 11th January Evening Slot
Question
A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant 2b from the origin. Then the locus of the centre of this circle, is :
Choose an option
Show full solutionCorrect option: B
Correct answer
Ba parabola
Step-by-step explanation
Let equation of circle is
x2 + y2 + 2fx + 2fy + e = 0, it passes through (0, 2b)
0 + 4b2 + 2g 0 + 4f + c = 0
4b2 + 4f + c = 0 . . . (i)
. . . (ii)
g2 c = 4a2 c =
Putting in equation (1)
4b2 + 4f + g2 4a2 = 0
x2 + 4y + 4(b2 a2) = 0, it represent a hyperbola.
x2 + y2 + 2fx + 2fy + e = 0, it passes through (0, 2b)
0 + 4b2 + 2g 0 + 4f + c = 0
4b2 + 4f + c = 0 . . . (i)
. . . (ii)
g2 c = 4a2 c =
Putting in equation (1)
4b2 + 4f + g2 4a2 = 0
x2 + 4y + 4(b2 a2) = 0, it represent a hyperbola.
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This is a previous-year question from JEE Main 2019, covering the Hyperbola chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.