If the focus of a hyperbola is (±3,0) and the equation of a…

Maths Conic Sections NTA Abhiyas Question - Hyperbola Single Correct MCQ

Published on: August 13, 2026

If the focus of a hyperbola is (±3,0) and the equation of a tangent is 2x + y - 4 = 0, then the equation of the hyperbola is

4x 2 - 5y 2 = 20

5x 2 - 4y 2 = 20

4x 2 - 5y 2 = 1

5x 2 - 4y 2 = 1

Text Solution

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The correct answer is:

4x 2 - 5y 2 = 20

Given, (±ae, 0) = (±3, 0)

ae= 3

….(i)

2x + y - 4 = 0

y=-2x + 4

is the tangent to the hyperbola

(4) 2 - a 2 (-2) 2 - 6 2 ( c 2 = a 2 m 2 - b 2 )

4a 2 - b 2 = 16 ...(ii)

On solving Eqs. (i) and (ii), we get,

a 2 =5, b 2 =4

Equation of hyperbola is

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