Question 1173706
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The asymptotes y=2x and y=-2x tell us that the center of the hyperbola is (0,0).<br>
With the foci in the x direction from the center (0,0), the equation is<br>
{{{x^2/a^2-y^2/b^2=1}}}<br>
The slopes of the asymptotes 2 and -2 tell us that b=2a; so the equation is<br>
{{{x^2/a^2-y^2/(4a^2)=1}}}<br>
The distance from the center to each focus, c, is 15; c is related to a and b by<br>
{{{c^2 = a^2+b^2}}}<br>
{{{c^2 = 225 = a^2+b^2 = a^2+4a^2 = 5a^2}}}
{{{a^2 = 45}}}<br>
The equation is<br>
{{{x^2/45-y^2/180 = 1}}}<br>