Hyperbola

Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6].

Result

h = (Correct answer is: )

Solution:

$$\begin{gathered} x_0={\displaystyle \frac{0+0}{2}}=0 \\ {y}_0={\displaystyle \frac{4\cdot \sqrt{6}+(-4)\cdot \sqrt{6}}{2}}=0 \\ S[0,0] \\ {{\displaystyle \frac{x-x_0}{a}}}^2-{{\displaystyle \frac{y-y_0}{b}}}^2=1 \\ {{\displaystyle \frac{x}{a}}}^2-{{\displaystyle \frac{y}{b}}}^2=1 \\ c=\sqrt{a^2+b^2} \\ h={{\displaystyle \frac{30}{a}}}^2-{{\displaystyle \frac{24}{b}}}^2=1 \end{gathered}$$

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