Explanation Given: The parabola equation is y = x 2 4 c with directrix y = − c , focus ( 0 , c ) and the vertex at the origin ( 0 , 0 ) . Calculation: Assume P ( x , y ) is a point on the parabola. The distance of the point P on the parabola from the focus is equal to its distance from the directrix. So, P F = P Q . Now, x 2 + ( y − c ) 2 = ( y + c ) 2 x 2 + y 2 − 2 c

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 12.5, Problem 75E

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We need to show that $y = \frac{x^{2}}{4 c}$ is the equation of a parabola with directrix $y = - c$ , $focus (0, c)$ and the vertex at the origin.

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Chapter 12.5, Problem 74E

Chapter 12.5, Problem 76E

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Chapter 12 Solutions

CALCULUS (CLOTH)

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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We need to show that y = x 2 4 c is the equation of a parabola with directrix y = − c , focus ( 0 , c ) and the vertex at the origin.

Solution Summary: The author explains the equation of a parabola with directrix y = c, focus, and the vertex at the origin.

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We need to show that $y = \frac{x^{2}}{4 c}$ is the equation of a parabola with directrix $y = - c$ , $focus (0, c)$ and the vertex at the origin.

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Chapter 12 Solutions

We need to show that y = x 2 4 c is the equation of a parabola with directrix y = − c , focus ( 0 , c ) and the vertex at the origin.

Solution Summary: The author explains the equation of a parabola with directrix y = c, focus, and the vertex at the origin.

Concept explainers

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We need to show that $y = \frac{x^{2}}{4 c}$ is the equation of a parabola with directrix $y = - c$ , $focus (0, c)$ and the vertex at the origin.