Explanation Given information: The equation is x 2 = 2 y . The given equation is in standard form x 2 = 4 p y . On comparing x 2 = 2 y with standard form, this will give 4 p = 2 Solve for p , Divide both the sides by 4 . 4 4 p = 2 4 p = 1 2 The parabola x 2 = 4 p y has y- axis symmetry and opens to the upward if p > 0 and to downward if p < 0 . Since, p is positive, the parabola opens to the upward with its y- axis symmetry. The focus of the parabola is 1 2 units to the upward of the vertex, ( 0 , 0 ) . The directrix is given by y = − p . Hence, the focus is ( 0 , 1 2 ) and directrix is y = − 1 2

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Chapter 8.2, Problem 7E

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To match the given equation with its graph and, also find the focus and directrix of the parabola with equation x2=2y.

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Chapter 8.2, Problem 6E

Chapter 8.2, Problem 8E

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Precalculus: A Unit Circle Approach

Ch. 8.2 - Prob. 1E Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E Ch. 8.2 - Prob. 5E Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Prob. 8E Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E

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To match the given equation with its graph and, also find the focus and directrix of the parabola with equation x 2 = 2 y .

Solution Summary: The author compares the given equation with its graph and finds the focus and directrix of the parabola with equation x2=2y.

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To match the given equation with its graph and, also find the focus and directrix of the parabola with equation x2=2y.

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