Graph: 16x2+25y2=400.

Short Answer

Expert verified

The graph of an ellipse is shown below:

Step by step solution

01

Given Information

The given ellipse is 16x2+25y2=400.

02

Step 2. Write the equation in standard form.

The standard form of an equation is x2a2+y2b2=1(1).

From(1),observe thatthe equation16x2+25y2=400is not in the standard form since both the xand yterms are squared and have different coefficients.

So, divide the equation 16x2+25y2=400both sides by 400to get the equation in standard form.

16x2400+25y2400=400400x225+y216=1

03

Step 3. Find whether the major axis is horizontal or vertical.

The equation x225+y216=1is in standard form centered at the origin.

So, compare the equation (1)with x225+y216=1to find a2and b2.

a2=25b2=16

Since 25>16and 25is in the x2term, the major axis will be horizontal.

04

Step 4. Find the endpoints of the major axis.

The endpoints will be the x-intercepts.

Since a2=25, a=±5.

Thus, the coordinates of the endpoints of the major axis are (5,0)and (-5,0).

05

Step 5. Find the endpoints of the minor axis.

The endpoints will be the y-intercepts.

Since b2=16, b=±4.

Thus, the coordinates of the endpoints of the minor axis are (0,4)and (0,-4).

06

Step 6. Draw the ellipse.

The graph of an ellipse is shown below:

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