Pre Calculus

Question

Given the equation of an ellipse, identify the center point: 4x² + 40x + 25y² - 100y + 100 = 0

Answer 1

Michael,

 

You must complete the square on x and y to do this.

 

Group the x and y-terms together, like this:

 

(4x² + 40x        ) + (25y² - 100y       ) = -100

 

Factor out the leading coefficient from each parenthesis group:

 

4(x² + 10x        ) + 25(y² - 4y       ) = -100

 

Complete each square (for x and y), by inserting half the middle coefficient squared:

 

4(x² + 10x + 25) + 25(y² - 4y + 4) = -100 + 100 + 100

 

Notice that I balanced the equation by adding the same amounts on the right side as well. This must be done to maintain equality.

 

Now, simplify:

 

4(x + 5)² + 25(y - 2)² = 100.

 

Put into standard form by dividing by 100:

 

(x + 5)²/25 + (y - 2)²/4 = 1.

 

This is the answer to your question. Please post a reply if you still need help with this.