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Hyperbola is at the center of coordinate system. Its foci (?) are on abscissa. There are two points on the hyperbola; these are $\displaystyle T_1(\frac{3\sqrt5}{2},2)$ and $\displaystyle T_2(4,\frac{4\sqrt7}{9})$. What is hyperbola's equation?
(I'm having trouble with solving two equations that follow(Headbang).)
Since its foci are on the abscissa [x-axis] and the hyperbola is centered at the origin, we know that the hyperbola has the form $\displaystyle \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, where $\displaystyle a>b$Quote:
Originally Posted by courteous
Now plug the two points into this equation, and you will generate two new equations:
At $\displaystyle \left(4,\frac{4\sqrt{7}}{9}\right)$, we get $\displaystyle \frac{16}{a^2}-\frac{112}{81b^2}=1$
At $\displaystyle \left(\frac{3\sqrt{5}}{2},2\right)$, we get $\displaystyle \frac{45}{4a^2}-\frac{4}{b^2}=1$
After solving the system of equations, I got $\displaystyle a=\sqrt{\frac{981}{53}}$
But I'm getting $\displaystyle b^2=-\frac{1744}{171}\implies b\text{ is complex.}$
Are you sure that you wrote down the coordinates correctly?
--Chris
Sorry!!!(Doh) No!!! Sorry, Chris!(Worried) The points are $\displaystyle T_1(\frac{3\sqrt5}{2},2)$ and $\displaystyle T_2(4,\frac{4\sqrt7}{3})$. The $\displaystyle T_2$ y-coordinate's denominator is 3 (not 9).Quote:
Originally Posted by Chris L T521
I've done it so many times that I've automatically restarted with partially already calculated number.(Speechless)
