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Chapter 10: Q 27. (page 643)

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

Vertex at0,0; axis of symmetry is y-axis ; containing the point2,3.

Short Answer

Expert verified

The equation of a parabola is x2=43y. The points are 23,-13and -23,-13.

The graph is

Step by step solution

01

Step 1. Given Information.

The vertex is 0,0and the axis of symmetry is y-axis andcontaining the point2,3.

02

Step 2. Equaion of a parabola.

The vertex is at the origin, the axis of symmetry is the y-axis, and the graph contains a point in the first quadrant, so the parabola opens up.

The form of the equation is

x2=4ay

Because the point 2,3is on the parabola, the coordinates are x=2,y=3must satisfy the equation x2=4ay. Substituting the values into the equation, we get

22=4a34=12aa=13.

The equation of the parabola isx2=43y.

03

Step 3. Latus Rectum.

The focus is at the point 0,13and the directix is the line y=-13. Letting y=13gives

x2=43yx2=4313x2=49x=卤23.

The points are23,13and-23,13.

04

Step 4. Graphing Utility.

The graph of a parabola is

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Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

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