Hyperbola equation

Find the hyperbola equation with the center of S [0; 0], passing through the points:
A [5; 3] B [8; -10]

Correct answer:

f : f = 7 * x^2 - 3y^2 = 148

Step-by-step explanation:

 a2(xx0)2  b2(yy0)2 = 1  a2x2  b2y2 = 1   52/a2  32/b2 = 1  82/a2  (10)2/b2 = 1  25/a2 = 1 +9/b2 a2 = 25 / (1 +9/b2)   64/25 (1 + 9/b2)  100/b2 = 1  64/25 (b2+9)100=b2  64/25 (b2+9)100=b2 1.56b276.96=0 b1,2=±76.96/1.56=±7.023769169 b1=7.023769169 b2=7.023769169  b=b1=7.02387.0238  a=25/(1+9/b2)=25/(1+9/7.02382)4.5981   x2/(148/7) y2/(148/3)=1  f:f=7 x23y2=148

Our quadratic equation calculator calculates it.




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