NIMCET 2023
The foci of the conic are
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option B —
Detailed Solution
Complete the squares: , so , i.e. .
This is a hyperbola with centre , , , and a horizontal transverse axis.
The foci are .
✓ Check
The vertex lies on the curve: .⚠ Common trap
(C) puts the foci on a vertical line; the positive term is , so the transverse axis is horizontal.Quick tip
; , foci
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Hyperbola — Preparation
This question tests your understanding of Hyperbola, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
A hyperbola is the set of points where the difference of the distances from two fixed points (the foci) is constant. Its standard form is x^2/a^2 - y^2/b^2 = 1, with eccentricity given by b^2 = a^2(e^2 - 1), where e > 1. The foci are at (ae, 0) and (-ae, 0), and the asymptotes are the lines y = (b/a)x and y = -(b/a)x. Exam questions test finding the foci, eccentricity, transverse and conjugate axes, latus rectum, asymptotes, and equations of tangents. A special case is the rectangular hyperbola, where a = b and e = sqrt 2. Many students confuse the hyperbola with the ellipse, so compare the signs in the equation and remember that the difference of focal distances equals 2a. Practise the hyperbola questions below, each with a step-by-step solution.