Find and Graph Equation of Ellipse?

Question

Find an equation for each ellipse below. Then, graph the equation.

(1) Foci at (1, 2) and (-3, 2); vertex at (-4, 2)

(2) Center at (1, 2); vertex at (1, 4) and passing through the point (2, 2)

Answer 1

(1) First, plot and label the points you know about. Then find the following:

The center (h,k) is midway between the foci

a is the distance between the vertex and the center

c is the distance between the center and either focus

b = sqrt(a² - c²)

The foci lie on the major axis, which in this case is horizontal, so the standard form for this ellipse is

(x-h)²/a² + (y-k)²/b² = 1

(2) Again, start by plotting and labeling the points you know about. Then find the following:

Center (h,k) = (1,2) is given

a is the distance from the vertex to the center

The center and vertex lie on the major axis, which in this case is vertical, so the standard form for the equation of this ellipse is

(x-h)²/b² + (y-k)²/a² = 1

The point (2,2) lies on the ellipse, so it satisfies the equation of the ellipse. This will enable you to find b.

Answer 2

you need to remodel what you have been given to the style you realize you want. that's further strategies which you need to renowned. a² > b² a² - b² = c² a = distance from midsection alongside important axis to vertices b = distance from midsection alongside minor axis to co-vertices c = distance from midsection alongside important axis to foci 9x² + 4y² = 36 -------> ÷ 36 x²/4 + y²/9 = a million b² = 4; a² = 9; c² = 5 b = 2; a = 3; c = ?5 important axis vertical midsection = (0, 0) vertices = (0, 3) (0, -3) foci = (0, ?5) (0, -?5) co-vertices = (2, 0) (-2, 0)