Question

the eccentricity of the hyperbola is 25x^2+y^2+200x-375=0 is

Answer 1

Step-by-step explanation:

I hope it helps you it is a hint for your question

Answer 2

Answer:

Eccentricity = $\sqrt{26}$

Step-by-step explanation:

25$x^{2}$ + $y^{2}$+ 200x -375 =0

Step-1:  $x^{2}$ + $\frac{y^{2} }{25}$ + 8x -15 = 0 [divided both sides by 25]

Step-2:  $x^{2}$ + $\frac{y^{2} }{25}$ + 8x +16 - 31 = 0

Step-3:  $x^{2}$ + 8x +16 + $\frac{y^{2} }{25}$  - 31 = 0

tep-5: $\frac{ (x+4)^2}{31}$ + $\frac{y^2}{775}$ = 1

a^2 = 31     b^2 = 775

Eccentricity = $\frac{\sqrt{a^2 + b^2}}{a}$  

                   = $\frac{\sqrt{31 + 775}}{\sqrt{31}}$

                   = $\sqrt{26}$