Question 735422
{{{(x^2)/(25)-(y^2)/(49)=1}}}
This is an equation of a hyperbola with horizontal transverse axis.
Its standard form:{{{(x-h)^2/a^2-(y-k)^2/b^2=1}}},(h,k)=(x,y) coordinates of center.
For given equation:
center:(0,0)
a^2=25
a=5
b^2=49
b=7
c^2=a^2+b^2=25+49=74
c=√74≈8.60
You got everything right except a and b which you had in reverse.
For hyperbolas, a and b don't change positions like in ellipses
For hyperbolas with vertical transverse axis, the y-term is placed ahead of the x-term, but a and b remain in the same position as that for a hyperbola with horizontal transverse axis