Question

36x^(2)-4y^(2)-36x-8y=31

explain conic hyperbola, help please

Answer 1

Explanation:

`36 {x}^(2) - 36x - 4 {y}^(2) - 8y = 31`

`) 36( {x}^(2) - x) - 4 ({y}^(2) + 2y )= 31`

For the x variables, after complete the square, you should get .

`36( {x}^(2) - x + (1)/(4) ) - 4( {y}^(2) + 2y) = 40`

Compete the square for y.

`36( (x)/(?) - x + (1)/(4) ) - 4( {y}^(2) + 2y + 1) = 36`

Next, simplify

`36(x - 0.5) {}^(2) - 4(y + 1) {}^(2) = 36`

Divide by 36b on both sides

`(x - 0.5) {}^(2) - \frac{(y + 1) {}^(2) }{9} = 1`

This is a hyperbola with a center of (0.5,-1),