Given that 4y^2+9x^2+16y+18x=k is an ellipse equation. Find the value of k.

Question

I want the steps. I want to know how to solve it. Thank you.

Answer 1

Given ellipse equation 4y^2+9x^2+16y+18x = k

9x^2+18x+4y^2+16y = k

To complete square add 17 to each side.

9x^2+18x+4y^2+16y+17 = k+17

9x^2+18x+4y^2+16y+9+8 = k+17

9(x^2+2x+1)+4(y^2+4y+2) = k+17

9(x+1)^2+4(y+2)^2 = k+17

⇒ k = 9(x+1)^2+4(y+2)^2-17

 

Answer 2

The ellipse equation is

To change the expressions (x ²- 2x) and (y ² + 4y) into a perfect square trinomial,

add (half the x coefficient)² and add (half the y coefficient)²to each side of the equation.