Question

What is the equation of a hyperbola with a = 5 and c = 15? Assume that the transverse axis is horizontal.

Answer 1

Answer:

$\frac{x^2}{25} -\frac{y^2}{200} =1$

Step-by-step explanation:

Recall that the equation of  hyperbola centered at the origin with transverse horizontal axis has the general form:

$\frac{x^2}{a^2} -\frac{y^2}{b^2} =1\\and\,\,\,\, with\\c=\sqrt{a^2+b^2}$

since we know that a = 5 ,and c = 15,we can solve for b:

$15=\sqrt{5^2+b^2} \\15^2=25+b^2\\b^2=200$

then the equation of the hyperbola becomes:

$\frac{x^2}{5^2} -\frac{y^2}{200} =1\\\frac{x^2}{25} -\frac{y^2}{200} =1$