Jimmy is designing a doghouse for his pet. He wants to determine the amount of overhang of the roof so that the shadow of the noonday sun reaches the bottom of the 6 foot wall during the summer months. The highest angle of the sun during the summer months is 75°. How much overhang does Jimmy need to provide for this purpose?

is the equation of an ellipse with directrices at x = ±4 and foci at (2, 0) and (−2, 0).

Step-by-step explanation:

It was given that, the ellipse has directrices at

The directrices has equation:

Where,  e is the eccentricity of the ellipse.

               >eq.1

Given the foci are (2, 0) and (−2, 0). It denotes (a e, 0) and (- a e, 0). Hence,

                a e = 2 >eq.2

Multiply eq. 1 and 2, we get

Taking square root, we get

Now substitute this ‘a’ value in eq. 2, we get

We know,

Substituting the values, we get

The equation for an ellipse is