Graph y^2=-36x

Problem

y^2=−36*x

Solution

1. Identify the type of conic section. The equation y^2=−36*x is in the standard form of a parabola that opens horizontally, y^2=4*p*x

2. Determine the value of p By comparing y^2=−36*x to y^2=4*p*x we set 4*p=−36

4*p=−36

p=−9

3. Locate the vertex. Since there are no h or k offsets in the equation, the vertex is at the origin.

Vertex=(0,0)

4. Find the focus and directrix. Since p=−9 and the parabola opens to the left, the focus is at (p,0) and the directrix is the vertical line x=−p

Focus=(−9,0)

Directrix:x=9

5. Identify points to define the width. The focal diameter (latus rectum) is |4*p|=36 Moving 18 units up and down from the focus gives the points (−9,18) and (−9,−18)

6. Sketch the graph. Draw a smooth curve starting at (0,0) that opens to the left, passing through (−9,18) and (−9,−18) with the focus at (−9,0) and the directrix at x=9

Final Answer

y^2=−36*x⇒Parabola opening left with vertex *(0,0), focus *(−9,0), and directrix *x=9

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