Question

Write an equation for the hyperbola.vertices (-5,0) and (5,0), foci (+V26,0)

Answer 1

$\frac{x^2}{25}-\text{ }\frac{y^2}{1}=\text{ 1}$Explanation:

Equation of hyperbola:

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

The vertices are (-5, 0) and (5, 0)

a = 5

-a = -5

Hence, a = 5

a² = 5² = 25

$\text{The foci = }\mleft(\pm\surd26,0\mright)$

foci = (26, 0) and (-26, 0)

c = √26

-c = -√26

So, c = √26

c² = (√26)² = 26

To get b:

c² = a² + b²

b² = c² - a²

b² = 26 - 25

b² = 1

b = √1 = +/- 1

Inserting the values the equation above:

$\frac{x^2}{25}-\text{ }\frac{y^2}{1}=\text{ 1}$