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: ) OK

Solution:

x0=0+02=0 y0=4⋅ 6+(−4)⋅ 62=0  S[0,0] x−x0a2−y−y0b2=1 xa2−yb2=1  c=a2+b2 h=30a2−24b2=1x_{0}=\dfrac{ 0+0 }{ 2 }=0 \ \\ y_{0}=\dfrac{ 4 \cdot \ \sqrt{ 6 }+(-4) \cdot \ \sqrt{ 6 } }{ 2 }=0 \ \\ \ \\ S[0,0] \ \\ \dfrac{ x-x_{0} }{ a } ^2-\dfrac{ y-y_{0} }{ b } ^2=1 \ \\ \dfrac{ x }{ a } ^2-\dfrac{ y }{ b } ^2=1 \ \\ \ \\ c=\sqrt{ a^2+b^2 } \ \\ h=\dfrac{ 30 }{ a } ^2-\dfrac{ 24 }{ b } ^2=1

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