# How do you find the sum of the coordinates of center in the conic #9x^2+25y^2-18x-150y+9=0#?

##### 1 Answer

#### Answer:

Here is a reference Conic section - General Cartesian form that gives the equation:

#### Explanation:

Here is a reference Conic section - General Cartesian form that gives the equation:

The given equation is:

We observe that

The reference tells us that this is an ellipse.

The standard Cartesian equation for and ellipse is:

where

Begin the conversion to this form by adding #9h^2 and 25k^2 to both sides of the equation and group all of the x terms and y terms together, respectively:

Remove a common factor of 9 from the first 3 terms and a common factor of 25 from the next 3 terms:

Using the pattern

The 9 on the left and the 9 on the right cancel:

Divide both sides by 25(9):

Write the denominators as squares:

This is an ellipse with the center at