Question

Write the equation -4x^2+9y^2+32x+36y-64=0 in standard form. Show each step of the process.

Answer 1

Answer:

The answer to your question is below

Step-by-step explanation:

      -4x² + 9y² + 32x + 36y - 64 = 0

     -4x² + 32x        + 9y² + 36y         =  64                          

     -4(x² + 8x        ) + 9(y² + 4x        ) = 64                     Factor coefficients

     -4(x² + 8x + 4²) + 9(y² + 4x + 2²) = 64 - 64 + 36     Complete trinomials

                -4(x + 4)² + 9(y + 2)² = 36                              Factor trinomials

    $\frac{-4(x+4)^{2} }{36} + \frac{9(y + 2)^{2} }{36} = \frac{36}{36}$

                                                                                       Divide by 36

    $- \frac{(x+ 4)^{2} }{9} + \frac{(y + 2)^{2} }{4} = 1$   Simplify