Answer:
[tex]\frac{x^2}{25} -\frac{y^2}{200} =1[/tex]
Step-by-step explanation:
Recall that the equation of hyperbola centered at the origin with transverse horizontal axis has the general form:
[tex]\frac{x^2}{a^2} -\frac{y^2}{b^2} =1\\and\,\,\,\, with\\c=\sqrt{a^2+b^2}[/tex]
since we know that a = 5 ,and c = 15,we can solve for b:
[tex]15=\sqrt{5^2+b^2} \\15^2=25+b^2\\b^2=200\\[/tex]
then the equation of the hyperbola becomes:
[tex]\frac{x^2}{5^2} -\frac{y^2}{200} =1\\\frac{x^2}{25} -\frac{y^2}{200} =1[/tex]
