Question

Find hyperbola equation. center (0,0) vertex (-2,0) focus (-5,0)

Answer 1

$\frac{ {x}^{2} }{4} - \frac{ {y}^{2} }{21} = 1$

<h2 />

$\frac{(x - h)^{2} }{ {a}^{2} } - \frac{(y - k) ^{2} }{ {b}^{2} } = 1$

a= (–2, 0) ; Center =(0,0)

$distance = \sqrt{(x2 - x1)^{2} + (y2 - y1) ^{2} } \\ a = \sqrt{(( - 2) - 0)^{2} + (0 - 0) ^{2} } \\ a = \sqrt{ {2}^{2} } \\ a = 2$

C = (–5,0) ; Center =(0,0)

$distance = \sqrt{(x2 - x1) ^{2} + (y2 - y1) ^{2} } \\ c = \sqrt{(( - 5) - 0)^{2} + (0 - 0) ^{2} } \\ c = \sqrt{ {5}^{2} } \\ c = 5$

C²= a²+ b²

(5)²= (2)² + b²

b²= 25–4 —> b² = 21

$b = + \sqrt{21} , - \sqrt{21}$

$m = \frac{y2 - y1}{x2 - x1} = \frac{0 - 0}{0 - ( -5 )} = 0$

$\frac{(x - h)^{2} }{ {a}^{2} } - \frac{(y - k) ^{2} }{ {b}^{2} } = 1$

$\frac{(x - 0)^{2} }{ {2}^{2} } - \frac{(y - 0) ^{2} }{ { \sqrt{2} }^{2} } = 1$

$\frac{ {x}^{2} }{4} - \frac{ {y}^{2} }{21} = 1$

I hope I helped you^_^