Question

Which graph represents the hyperbola? x^2/5^2 - y^2/4^2 = 1

Answer 1

When it's x²/a² - y²/b²=1 it's the one with zeros on the x axis, at x=±a, y=0.

Here the zeros are at (±5,0) so that's the first page, second graph.

Answer 2

A hyperbola is a two-branched open curve created by the intersection of a circular cone with a plane that cuts both nappes. The correct option is B.

What is a Hyperbola?

A hyperbola is a two-branched open curve created by the intersection of a circular cone with a plane that cuts both nappes.

As per the general equation of hyperbola,

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

a and b are the length and the width of the rectangle in the middle of the graph respectively.

As here the value of a and b is 5 and 4, respectively. Therefore, the graph of the hyperbola $\dfrac{x^2}{5^2} - \dfrac{y^2}{4^2} = 1$ will have a rectangle with a horizontal length of 5 and vertical width of 4 units in between the graph.

Hence, the correct option is B.

Learn more about Hyperbola:

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