For Exercise, an equation of a degenerate conic section is given. Complete the square and describe the graph of each equation.

Bergen
2020-12-28
Answered

For Exercise, an equation of a degenerate conic section is given. Complete the square and describe the graph of each equation.

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SchulzD

Answered 2020-12-29
Author has **83** answers

Step 1

The given equation is$9{x}^{2}+4{y}^{2}-24y+36=0.$

Use completing the square method and obtain the standard form

Step 2

$4{y}^{2}-24y=-9{x}^{2}-36$

$4({y}^{2}-6y)=-9{x}^{2}-36$

$4({y}^{2}-6y+{3}^{2}-{3}^{2})=-9{x}^{2}-36$

$4{(y+3)}^{2}-36=-9{x}^{2}-36$

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

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

$y+3=-\frac{3}{2}x$

$2y+6=-3x$

$4x+2y+6=0$

Step 3

Draw the graph of$4x+2y+6=0$

The given equation is

Use completing the square method and obtain the standard form

Step 2

Step 3

Draw the graph of

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