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QuestionFind the intercepts of the equation 9x2+4y2=369 x^{2}+4 y^{2}=36. A. List them as ordered pairs. B. Or state there are none.

Studdy Solution

STEP 1

Assumptions1. We are dealing with a plane (x, y). . The intercepts are the points where the graph of the equation intersects the x-axis and y-axis.
3. An x-intercept is a point where y =0, and a y-intercept is a point where x =0.

STEP 2

To find the x-intercepts, we set y =0 in the equation and solve for x.
9x2+4(0)2=369x^{2} +4(0)^{2} =36

STEP 3

implify the equation.
9x2=369x^{2} =36

STEP 4

To isolate x, divide both sides of the equation by9.
x2=369x^{2} = \frac{36}{9}

STEP 5

olve for x.
x2=4x^{2} =4

STEP 6

Take the square root of both sides. Remember to consider both the positive and negative roots.
x=±4x = \pm \sqrt{4}

STEP 7

Calculate the x-intercepts.
x=±2x = \pm2

STEP 8

To find the y-intercepts, we set x =0 in the equation and solve for y.
(0)2+4y2=36(0)^{2} +4y^{2} =36

STEP 9

implify the equation.
4y2=364y^{2} =36

STEP 10

To isolate y, divide both sides of the equation by4.
y2=364y^{2} = \frac{36}{4}

STEP 11

olve for y.
y=9y^{} =9

STEP 12

Take the square root of both sides. Remember to consider both the positive and negative roots.
y=±9y = \pm \sqrt{9}

STEP 13

Calculate the y-intercepts.
y=±3y = \pm3The intercepts of the equation are (2,0), (-2,0), (0,3), and (0, -3).

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