Graph x^2=8y

Problem

x2=8*y

Solution

1. Identify the type of conic section. The equation x2=8*y is in the standard form of a parabola that opens vertically, x2=4*p*y

2. Determine the value of p By comparing x2=8*y to x2=4*p*y we set 4*p=8 which gives p=2

3. Locate the vertex and focus. Since there are no shifts, the vertex is at (0,0) Because p=2 and the parabola opens upward, the focus is at (0,p) which is (0,2)

4. Find the directrix. The directrix is a horizontal line located p units below the vertex, given by the equation y=−p so y=−2

5. Calculate the endpoints of the latus rectum. The latus rectum has a total length of |4*p|=8 Starting from the focus (0,2) move 4 units to the left and 4 units to the right to find the points (−4,2) and (4,2)

6. Sketch the curve. Draw a smooth curve starting from the vertex (0,0) passing through the points (−4,2) and (4,2) opening upwards toward the focus.

Final Answer

x2=8*y⇒y=1/8*x2

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