Ive included an elarged image of the graph Write an equation

I\'ve included an elarged image of the graph.

Write an equation for the ellipse. Type the left side of the equation in the box below. Q.

Solution

equation of ellipse is given by

(x - h)^2/a^2 + (y - k)^2/b^2 = 1

here,

2a = 6 So, a = 3

2b = 8 So, b = 4

(x - h)^2/9 + (y - k)^2/16 = 1

Since it passes from (0, 0)

h^2/9 + k^16 = 1

Also, it passes through (3, 4)

(h - 3)^2/9 + (k - 4)^2/16 = 1

Solving both equation

h = 3 and k = 0

So, equation of ellipse will be

(x - 3)^2/9 + (y)^2/16 = 1