Hyperbola equation

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

Result

f = (Correct answer is: f = 7 * x^2 - 3y^2 = 148) Wrong answer

Solution:

(x−x0)2a2−(y−y0)2b2=1  x2a2−y2b2=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 1.56b2−76.96=0  p=1.56;q=0;r=−76.96 D=q2−4pr=02−4⋅1.56⋅(−76.96)=480.2304 D>0  b1,2=−q±D2p=±480.233.12 b1,2=±7.02376916857 b1=7.02376916857 b2=−7.02376916857   Factored form of the equation:  1.56(b−7.02376916857)(b+7.02376916857)=0  b=b1=7.0238≐7.0238   a=25/(1+9/b2)=25/(1+9/7.02382)≐4.5981  x2/(148/7)−y2/(148/3)=1  f=7⋅ x2−3y2=148

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