Convert the equation to the standard form for a hyperbola 4x^2-25y^2-8x+50y-121=0

We have that
4x²-25y²-8x+50y-121=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation
(4x²-8x)+(-25y²+50y)=121

Factor the leading coefficient of each expression
4(x²-2x)-25(y²-2y)=121

Complete the square twice. Remember to balance the equation by adding the same constants to each side.
4(x²-2x+1)²-25(y²-2y+1)²=121+4-25

Rewrite as perfect squares
4(x-1)²-25(y-1)²=100

Divide both sides by the constant term to place the equation in standard form
(4/100)(x-1)²-(25/100)(y-1)²=100/100
(1/25)(x-1)²-(1/4)(y-1)²=1

[(x-1)²]/25-[(y-1)²]/4=1

the answer is
[(x-1)²]/25-[(y-1)²]/4=1

In all honesty, there really is no “work” per say to show. mainly it’s just using the process of elimination. the question is asking which domain(s) would be the most appropriate for the function c(n). n is the number of observed vehicles so right away, 1, 2, and 3 can be eliminated.why? 1, 2 start in the negatives and therefore it is impossible to observe negative cars. so, #4 would be the best answer to the given problem.