Question

Write the equation 16x2 + 25y2 − 32x + 50y + 16 = 0 in vertex form.

Answer 1

Solution

We have the following equation given:

$16x^2+25y^2-32x+50y+16=0$

We can complte the squares and we have this:

$16(x^2-2x)+25(y^2+2y)+16=0$$16(x^2-2x+1)+25(y^2+2y+1)+16=16+25$

And then if we simplify we got:

$16(x-1)^2+25(y+1)^2=25$$\frac{(x+1)^2}{(\frac{5}{4})^2}+\frac{(y+1)^2}{1}=1$