### Home > A2C > Chapter Ch11 > Lesson 11.3.3 > Problem 11-157

11-157.

Identify the shape of the graph of each equation below, change it to graphing form (if necessary), and sketch a graph. Homework Help ✎

2

*y*^{2}−*x*+ 4*y*+ 2 = 05

*x*+ 2*y*− 10 = 04

*x*^{2}+ 4*y*^{2}+ 4*x*− 24*y*+ 21 = 09

*x*^{2}− 16*y*^{2}+ 54*x*− 32*y*+ 29 = 09

*x*^{2}+ 4*y*^{2}+ 54*x*− 16*y*+ 97 = 04

*x*^{2}−*y*^{2}+ 24*x*+ 36 = 0

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

*x* = 2(*y* + 1)^{2}

2*y* = −5*x* + 10

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

4(*x*^{2} + *x*) + 4(*y*^{2} − 6*y*) = −21

= − 21 + 1 + 36

See part (c).

See part (c).

9(*x*^{2} + 6*x*) + 4(*y*^{2} − 4*y*) + 97 = 0

9(*x*^{2} + 6*x* + 9) − 81 + 4(*y*^{2} − 4*y* + 4) − 16 + 97 = 0

9(*x* + 3)^{2} + 4(*y* − 2)^{2} = 0

See part (c).

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