Question

Which of the following is the equation for the graph shown?

graph of horizontal hyperbola on a coordinate plane going through 2 comma 0 and negative 2 comma 0 with points at negative 4 comma 0 and 4 comma 0, lines at x equals 1 and x equals negative 1

y squared over 4 minus x squared over 12 equals 1
y squared over 16 minus x squared over 12 equals 1
x squared over 4 minus y squared over 12 equals 1
x squared over 16 minus y squared over 12 equals 1

Answer 1

The equation of the hyperbola is $\frac{x^2}{4} -\frac{y^2}{12} = 1$

How to determine the equation of the graph?

The points on the graph are given as:

• (2, 0) and (-2, 0)
• (4, 0) and (-4, 0)
• Lines at: x = 1 and x = -1

The hyperbola can be represented as:

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

The points (2, 0) and (-2, 0) means that:

$b = \±2$

Square both sides

$b^2 = 4$

So, we have:

$\frac{x^2}{4} -\frac{y^2}{a^2} = 1$

Also, we have:

a^2 = c^2 - b^2

Where c = 4

This gives

a^2 = 4^2 - 4

Evaluate

a^2 = 12

Substitute a^2 = 12 in $\frac{x^2}{4} -\frac{y^2}{a^2} = 1$

$\frac{x^2}{4} -\frac{y^2}{12} = 1$

Hence, the equation of the hyperbola is $\frac{x^2}{4} -\frac{y^2}{12} = 1$

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