Graph x^2=12y

Problem

x2=12*y

Solution

1. Identify the type of conic section. The equation x2=12*y is in the standard form of a parabola that opens vertically, x2=4*p*y

2. Determine the value of p By comparing 4*p=12 we find p=3 Since p>0 the parabola opens upward.

3. Locate the vertex. Since there are no h or k offsets, the vertex is at the origin (0,0)

4. Find the focus and directrix. The focus is at (0,p) which is (0,3) The directrix is the horizontal line y=−p which is y=−3

5. Calculate the endpoints of the latus rectum. The length of the latus rectum is |4*p|=12 Moving 6 units to the left and right of the focus (0,3) gives the points (−6,3) and (6,3)

6. Sketch the curve. Draw a smooth curve starting at the vertex (0,0) passing through the points (−6,3) and (6,3) and opening upward around the focus.

Final Answer

x2=12*y⇒Parabola with vertex *(0,0), focus *(0,3), and directrix *y=−3

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