(a) Use rotation of axes to show that the following equation represents a parabola. (Write the equation in XY-coordinates. Use a rotation angle that satisfies 0 ≤ ≤ 7/2 and that eliminates the xy-term. 2√2(x + y)² = 7x + 9y (b) Find the XY- and xy-coordinates of the vertex and focus. XY-coordinates vertex focus (c) Find the equation of the directrix in XY- and xy-coordinates. XY-coordinates (x, y) = ( (x, y) = ( [ xy-coordinates xy-coordinates (x, y) = ( (x, y) = ( |) 응 0⁰
(a) Use rotation of axes to show that the following equation represents a parabola. (Write the equation in XY-coordinates. Use a rotation angle that satisfies 0 ≤ ≤ 7/2 and that eliminates the xy-term. 2√2(x + y)² = 7x + 9y (b) Find the XY- and xy-coordinates of the vertex and focus. XY-coordinates vertex focus (c) Find the equation of the directrix in XY- and xy-coordinates. XY-coordinates (x, y) = ( (x, y) = ( [ xy-coordinates xy-coordinates (x, y) = ( (x, y) = ( |) 응 0⁰
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:(a) Use rotation of axes to show that the following equation represents a parabola. (Write the equation in XY-coordinates. Use a rotation angle that satisfies 0 ≤ ≤ π/2 and that eliminates the xy-term.)
2√2(x + y)² = 7x + 9y
(b) Find the XY- and xy-coordinates of the vertex and focus.
XY-coordinates
vertex
focus
XY-coordinates
(X, Y):
(c) Find the equation of the directrix in XY- and xy-coordinates.
xy-coordinates
(X,Y)=
xy-coordinates
(x, y) = ([
(x, y) =
=([
X
|-|-
00
Transcribed Image Text:(b) vertex (hik)=
(Ⓒ)
So
Росия
and
=
(X,Y)= (1,4) 1
(2₁4) = (1, 6¾/16)
(X,Y)= (-3/₂15/₂)
Equation of directrix
(9₁9) = (-01 1/12)
y = c = (6²71) 49
Y = or (8² +1) 4 (-4) = 1040
y-x = 1040-√2
y
Y = 1040√√2 +7
LAVE
1-47 79
16√2
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