PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Question
Chapter 9.1, Problem 60E
To determine
To find: The vertex, focus and directrix of the parabola x+y2=0 and verify with the help of graphing utility.
Expert Solution & Answer
Answer to Problem 60E
The vertex, focus and directrix of the parabola x+y2=0 are (0,0) , (−14,0) , x=14 respectively. The graph of the parabola with vertex, focus and directrix is shown in Figure (1).
Explanation of Solution
Given information:
The equation of the parabola is x+y2=0 .
Calculation:
Simplify the equation of the parabola.
x+y2=0y2=−x
Compare the given equation of parabola with general horizontal axis parabola equation (y−k)2=4p(x−h) . This gives the value of h , k , p as 0 , 0 , −14 respectively.
The vertex of the parabola x+y2=0 is (h,k)=(0,0) .
The focus of the horizontal axis parabola x+y2=0 is:
(h+p,k)=(0+(−14),0)=(−14,0)
The directrix of the parabola x+y2=0 is:
x=h−p=0−(−14)=14
Therefore, the vertex, focus and directrix of the parabola x+y2=0 are (0,0) , (−14,0) , x=14 respectively.
The graph of the parabola x+y2=0 with vertex, focus and directrix is shown below.
Figure (1)
Here we can verify the vertex, focus, directrix of the parabola x+y2=0 are (0,0) , (−14,0) , x=14 respectively.
Chapter 9 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
Ch. 9.1 - Prob. 1ECh. 9.1 - Prob. 2ECh. 9.1 - Prob. 3ECh. 9.1 - Prob. 4ECh. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - Prob. 7ECh. 9.1 - Prob. 8ECh. 9.1 - Prob. 9ECh. 9.1 - Prob. 10E
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- 16. The appropriate form for the particular solution yp(x) of y^(3) − y′′ − 2y′ = x^2 + e^2x isA. yp(x) = Ax^2 + Bx + C + De^2x B. yp(x) = Ax^3 + Bx^2 + Cx + Dxe^2xC. yp(x) = Ax^2 +Be^2x D. yp(x) = A+Be^2x +Ce^−x E. yp(x) = Ax^2 +Bx+C +(Dx+E)e^2xarrow_forwardDistance Between Two Ships Two ships leave the same port at noon. Ship A sails north at 17 mph, and ship B sails east at 11 mph. How fast is the distance between them changing at 1 p.m.? (Round your answer to one decimal place.) 20.3 X mph Need Help? Read It Watch It SUBMIT ANSWERarrow_forwardpractice problem please help!arrow_forward
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