How do I find the vertices, co-vertices and foci of a Ellipse circle?
To find the vertices, look at the denominators. Take the square root and go that many units on either side of the center in the direction of the variable in the numerator. In your example, the denominator in the “x” fraction is 16, so you would go 4 units on either side of the center in the x direction to get (-6, 3) and (2, 3). For the “y” fraction, the denominator is 36, so you would go 6 units on either side of the center in the y direction to get (-2, -3) and (-2, 9). To find the foci, subtract the denominators, then take the square root of your answer, then go that many units on either side of the center in the direction where you went the farthest to find the vertices. In your example, 36-16=20. Square root 20 = 4.47 You went the farthest in the y direction, so go 4.47 units up from the center and 4.47 units down from the center to get (-2, -1.47) and (-2, 7.47) Good luck on your test!
