CPM Homework Help : A2C Problem 11-142

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Home > A2C > Chapter Ch11 > Lesson 11.3.2 > Problem 11-142

11-142.

Change each of the following equations to graphing form, identify the conic, and sketch the graph. Homework Help ✎
1. 4x² − y² − 24x − 10y = 5
2. x² + y + 10x − 4y = −13
3. 4x² + 9y² + 24x − 36y = −36
4. 3x² − 12x − y = −17

Hint (a):

4(x² − 6x + 9) − (y² + 10y + 25) = 5 + 36 − 25

More Help (a):

4(x − 3)² − (y + 5)² = 16

Answer (a):

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

This is a hyperbola.

Hint (b):

See part (a).

Answer (b):

(x + 5)² + (y − 2)² = 16
This is a circle.

Hint (c):

See part (a).

Answer (c):

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

This is an ellipse.

Hint (d):

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

Answer (d):

y = 3(x − 2)² + 5
This is a parabola.

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