Focus is at $F\equiv(−3−3√13, 1)$, asymptotes intersect at the point with coordinates $(−3, 1)$ and one asymptote passes through $(1, 7)$
I've solved some problems that involve equations of hyperbolas but this one got me stumped.
2026-04-09 07:25:37.1775719537
Find the equation of the hyperbola that satisfies this condition
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$(-3,1)$ is center.
the two asymtotes are lines passing through $(-3,1)$. One passes through $(1,7)$ , other through focus , write their equation, find angle between them ($\theta$), then eccentricity is $\sec\theta/2$.
length of semi-major axis is distance between center and focus.
Now you have everything you need.