Exercise 10 Page 85

Before we begin, note that in the given equation the variable that is raised to the second power is x. 36y=x^2 Therefore, the axis of symmetry of the parabola is a vertical line.

Finding the Desired Information

Let's recall the general form of the equation for this type of parabola. y= 1/4 * p(x- h)^2+ k In order to match this form perfectly, let's rewrite our equation. 36y=x^2 ⇔ y= 1/36x^2 We need to identify the values of p, h, and k. Let's start with p. To do so, we will solve the equation 14 p=136. We set it equal to 136, because it is the coefficient of the parenthetical factor.

Knowing that p= 9, we can rewrite the equation. y= 1/36x^2 ⇕ y= 1/4 * 9(x- 0)^2+ 0 Now we can see that p= 9, h= 0, and k= 0. By recalling the corresponding formulas we can find the focus, directrix, and axis of symmetry of the parabola.

Drawing the Parabola

Now, let's draw the parabola using the obtained information.