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)2b2(yy0)2=1  a2x2b2y2=1  52/a232/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  p=1.56;q=0;r=76.96 D=q24pr=0241.56(76.96)=480.2304 D>0  b1,2=2pq±D=3.12±480.23 b1,2=±7.0237691685685 b1=7.0237691685685 b2=7.0237691685685   Factored form of the equation:  1.56(b7.0237691685685)(b+7.0237691685685)=0  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

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