JEE Main · 2026 · 23 Jan 2026 · Shift 1 · Ellipse

Let the line

y - x = 1

intersect the ellipse

\frac{x ^{2}}{2} + \frac{y ^{2}}{1} = 1

at the points A and B. Then the angle made by the line segment AB at the center of the ellipse is :

Answer: (B)

Solution

Substitute

y = x + 1

into the ellipse equation:

\frac{x ^{2}}{2} + (x + 1)^{2} = 1

.

Expanding:

\frac{x ^{2}}{2} + x^{2} + 2 x + 1 = 1

, so

\frac{3 x ^{2}}{2} + 2 x = 0

, giving

x = 0

x = - \frac{4}{3}

.

The points are

A (0, 1)

and

B (- \frac{4}{3}, - \frac{1}{3})

.

Slope of OB:

tan θ = \frac{- 1/3}{- 4/3} = \frac{1}{4}

.

Since OA is along the positive y-axis and the line has slope 1, the angle

∠ A O B = \frac{π}{2} + tan^{- 1} (\frac{1}{4})

JEE Main · 2026 · 23 Jan 2026 · Shift 1 · Single correct option