# How do you find the coordinates of the center, foci, the length of the major and minor axis given #3x^2+y^2+18x-2y+4=0#?

##### 1 Answer

Given:

Center:

Foci:

major axis = 2a

minor axis = 2b

#### Explanation:

The following are the steps to put the given equation into the form of equation [1]:

Subtract 4 from both sides:

Group the x terms and the y terms together on the left:

Because the coefficient of the x^2 term is 3, add #3h^2 to both sides ; make it the 3rd term on the left and the first term on the right:

Because the coefficient of the y^2 term is 1, add k^2 to both sides; make it the sixth term on the left and the second term on the right:

Remove a common factor of 3 from the first 3 terms:

Use the pattern for

Match the "-2hx" term in the pattern with the "6x" term in equation [6] and write the equation:

Solve for h:

This means that we can substitute

Use the pattern for

Match the "-2ky" term in the pattern with the "-2y" term in equation [7] and write the equation:

Solve for k:

This means that we can substitute

Simplify the right:

Divide both sides by 6:

Swap terms and write the denominators as squares:

We have the form of equation [1]

Center:

Foci:

Major axis:

Minor axis: