$2y^{2} + 4y + 2 = x$

$x = 2\left(y + 1\right)^{2}$

$2y = −5x + 10$

Try to factor and complete the squares for x and y.

4(x² + x) + 4(y² − 6y) = −21

$4\left(x^2+x+\frac{1}{4}\right)+4(y^{2}-6y+9)$

= − 21 + 1 + 36

$\left(x+\frac{1}{2}\right)^2+(y-3)^2=4$

See part (c).

See part (c).

$9\left(x^{2} + 6x\right) + 4\left(y^{2} − 4y\right) + 97 = 0$$9\left(x^{2} + 6x + 9\right) − 81 + 4\left(y^{2} − 4y + 4\right) − 16 + 97 = 0$

$9\left(x + 3\right)^{2} + 4\left(y − 2\right)^{2} = 0$

See part (c).

Notice that $y ^{2}$ is the only term containing y. Try to get it by itself.