1. Write the equation that models the height of the roller coaster. Start by writing the equation of the circle. (Recall that the general form of a circle with the center at the origin is x2 + y2 = r2. (10 points) Now solve this equation for y. Remember the roller coaster is above ground, so you are only interested in the positive root. (10 points)

a.)x² + y² = 900

b.)y = √900 - x²

Step-by-step explanation:

P.S - The exact equation is as follows :

As given,

The shape of the roller coaster is a half of a circle. Center the circle at the origin and assume the highest point on this leg of the roller coaster is 30 feet above the ground.

a.)

Equation of circle be x² + y² = r²

As given , leg of the roller coaster is 30 feet above the ground.

⇒ r = 30

⇒x² + y² = 30²

⇒x² + y² = 900

∴ we get

Equation of height of Roller coaster - x² + y² = 900

b.)

As we have,  x² + y² = 900

⇒y² = 900 - x²

⇒y = √900 - x²