MathsJEE Main 23 Jan 2026, Shift 2·Q8·MCQ·Moderate

Conic Sections · Curves through intersection points

If the points of intersection of the ellipses

x^2 + 2y^2 - 6x - 12y + 23 = 0

and

4x^2 + 2y^2 - 20x - 12y + 35 = 0

lie on a circle of radius

r

and centre

(a, b)

, then the value of

ab + 18r^2

(1)53
(2)51
(3)52
(4)55

We corrected a printing error in the original paper

Source printed “ $4x + 2y^2 - 20x - 12y + 35 = 0$ ”; corrected to the intended “ $4x^2 + 2y^2 - 20x - 12y + 35 = 0$ ” (as printed the second curve is a parabola, not an ellipse, and meets the first in only two points, so the circle is not determined).

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