Find an equation for the conic whose graph is shown 10 15 10

Find an equation for the conic whose graph is shown.

Solution

(x-6.5)²/a² - y²/b² = 1

a = 6.5 - 3 = 3.5

(x-6.5)²/3.5² - y²/b² = 1

now it passes through (0,6)

(0-6.5)²/3.5² - 6²/b² = 1 => 3.834

=>(x-6.5)²/3.5² - y²/3.834² = 1