### Home > A2C > Chapter 11 > Lesson 11.3.2 > Problem11-142

11-142.

Change each of the following equations to graphing form, identify the conic, and sketch the graph.

1. $4x^{2} − y^{2} − 24x − 10y = 5$

$4\left(x^{2} − 6x + 9\right) − \left(y^{2} + 10y + 25\right) = 5 + 36 − 25$

$4\left(x − 3\right)^{2} − \left(y + 5\right)^{2} = 16$

$\frac{(x-3)^2}{4}-\frac{(y+5)^2}{16}=1$

This is a hyperbola.

1. $x^{2} + y + 10x − 4y = −13$

See part (a).

$\left(x + 5\right)^{2} + \left(y − 2\right)^{2} = 16$
This is a circle.

1. $4x^{2} + 9y^{2} + 24x − 36y = −36$

See part (a).

$\frac{(x+3)^2}{9}+\frac{(y-2)^2}{4}=1$

This is an ellipse.

1. $3x^{2} − 12x − y = −17$

Set the equation equal to y and complete the square for x.

$y = 3\left(x − 2\right)^{2} + 5$
This is a parabola.