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COMEDK 2025 Afternoon Solved Paper

Question : 128 of 180

Marks: +1, -0

49 y^2-16 x^2=784

Solution:

Concept:

The given equation represents a hyperbola; its latus rectum length is

\frac{2b^2}{a}

for the standard form

\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1

Explanation:

First, rewrite the equation

49y^2 - 16x^2 = 784

in standard form.

Divide both sides by 784 to get

\frac{49y^2}{784} - \frac{16x^2}{784} = 1

Simplify each term:

\frac{y^2}{16} - \frac{x^2}{49} = 1

Thus,

a^2 = 16

(under

y^2

) and

b^2 = 49

(under

x^2

), so

a = 4

and

b = 7

For a hyperbola in the form

\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1

, the length of each latus rectum is

\frac{2b^2}{a}

Substitute

b^2 = 49

and

a = 4

\frac{2 \times 49}{4} = \frac{98}{4} = \frac{49}{2}

Answer:

\frac{49}{2}

(Option A).

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