Find the foci of the equation 25^2 + x^2 = 600

Thank you!

did you mean

25y^2 + x^2 = 600 ?

please confirm before I proceed

Yes

divide both sides by 600

y^2 /24 + x^2 /600 = 1

so a^2 = 600 and b^2= 24
in this case
b^2 + c^2= a^2
24 + c^2= 600
c^2 = 576
c= ±√576 = ±24

the foci are (24,0) and (-24,0)

To find the foci of the equation, we first need to rewrite it in standard form. The given equation is:

25^2 + x^2 = 600.

We can simplify this equation to:

625 + x^2 = 600.

Rearranging the terms, we get:

x^2 = 600 - 625.

Simplifying further, we have:

x^2 = -25.

To isolate x, we take the square root of both sides:

x = ±√(-25).

However, taking the square root of a negative number results in imaginary solutions, which means there are no foci.

Therefore, the equation 25^2 + x^2 = 600 does not have any foci.