Graph x^2=9y

Problem

x2=9*y

Solution

1. Identify the type of conic section. The equation is in the form x2=4*p*y which represents a parabola that opens vertically.

2. Determine the vertex. Since there are no h or k offsets in the equation, the vertex is at the origin (0,0)

3. Find the value of p Set the coefficient of y equal to 4*p

4*p=9

p=9/4=2.25

4. Locate the focus and directrix. Since p is positive and the parabola opens upward, the focus is at (0,p) and the directrix is the horizontal line y=−p

Focus=(0,2.25)

Directrix:y=−2.25

5. Calculate additional points to define the width. Choose y values that make x easy to calculate, such as y=1 and y=4

If *y=1,x2=9⇒x=±3

If *y=4,x2=36⇒x=±6

6. Sketch the graph by plotting the vertex (0,0) the points (3,1) (−3,1) (6,4) and (−6,4) and drawing a smooth upward-opening curve through them.

Final Answer

x2=9*y⇒y=1/9*x2

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