IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Quant & DI · Question 2

IIM B UG (B.Sc-Hons.)- Sample Paper 2026 question on Conic Sections, with the answer and a step-by-step solution.

Conic SectionsCoordinate GeometryMultiple choiceMedium
An ellipse has foci at (−3, 0) and (3, 0), and passes through \left( 3, \frac{16}{5}\right). What is the length of its latus rectum?
  1. A
    \frac{18}{5}
  2. B
    \frac{32}{5}
  3. C
    \frac{25}{4}
  4. D
    \frac{16}{5}
Pick an option, then check.
Answer & solution

Answer: Option B

The foci lie on the x-axis at (±3, 0), so c = 3 and the ellipse is x²/a² + y²/b² = 1 with a² = b² + 9.

The given point has x = 3, which is exactly x = c, so its y-coordinate is the semi-latus rectum b²/a.

Therefore b²/a = 16/5, that is b² = 16a/5.

Substituting into a² = b² + 9 gives a² = 16a/5 + 9, or 5a² − 16a − 45 = 0.

Solving: a = (16 + √1156)/10 = (16 + 34)/10 = 5.

Then b² = 16 × 5 ÷ 5 = 16.

Length of the latus rectum = 2b²/a = 32/5.

Take this paper as a timed test
Real exam timing, instant score, rank and topic-wise analysis.

Practice timed →