# How do you graph #4x^2+49y^2+294y+245=0#?

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identify the center, vertices, co-vertices, foci, and eccenticity of each

identify the center, vertices, co-vertices, foci, and eccenticity of each

##### 1 Answer

Use the discriminant to identify the equation as an ellipse

Complete the squares to obtain the standard form

#### Explanation:

In the section entitled [General Cartesian Form](https://en.wikipedia.org/wiki/Conic_section

We observe that for the equation

In the section entitled [Discriminant](https://en.wikipedia.org/wiki/Conic_section

Substitute

The same section tells us that if the discriminant is negative and

In either case, we must complete the squares, using the patterns,

Subtract 245 from both sides:

The fact that

Because

This tells us that we must add

We can find the value of k by set the middle term in the right side of the pattern equal to the middle term in the equation:

Substitute the left side of the pattern into the left side of the equation and substitute

Simplify the right side:

Divide both sides of the equation by 196:

Write the denominators as squares:

The following is the graph:

graph{(x-0)^2/7^2+(y- (-3))^2/2^2=1 [-7.51, 8.294, -6.807, 1.09]}

The center is the point

The vertices are the points

The covertices are the points

The foci are the points

The eccentricity is: