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.