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(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 s os x/2 and that eliminates the xy-term.) 2√2(x + y)² = 7x + 9y (x-1)² = (4-Y) (b) Find the XY- and xy-coordinates of the vertex and focus. XY-coordinates vertex focus XY-coordinates xy-coordinates X (X,Y)=(1,-4 Need Help? Read It 65√2 16 (x, y) = (1,5 (c) Find the equation of the directrix in XY- and xy-coordinates. 65√/2 16 -63 16 X X ✓) ✓ (x, y) = ( (x, y) = ( xy-coordinates 5√2 2' 79√/2 32 " 3√2 2 47√/2 32 )

(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 s os x/2 and that eliminates the xy-term.) 2√2(x + y)² = 7x + 9y (x-1)² = (4-Y) (b) Find the XY- and xy-coordinates of the vertex and focus. XY-coordinates vertex focus XY-coordinates xy-coordinates X (X,Y)=(1,-4 Need Help? Read It 65√2 16 (x, y) = (1,5 (c) Find the equation of the directrix in XY- and xy-coordinates. 65√/2 16 -63 16 X X ✓) ✓ (x, y) = ( (x, y) = ( xy-coordinates 5√2 2' 79√/2 32 " 3√2 2 47√/2 32 )

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.6: Quadratic Functions
Problem 34E
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(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 (x-1)² = ¹/(4-Y) (b) Find the XY- and xy-coordinates of the vertex and focus. vertex focus XY-coordinates xy-coordinates Need Help? X (x, y) = Read It (x, y) = 65√2 16 (c) Find the equation of the directrix in XY- and xy-coordinates. 65√2 16 XY-coordinates 1,- 4 1, -63 16 (x, y) = = (x, y) xy-coordinates 5√2 2 79√2 32 9 2 3√2 2 47√2 32
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 (x-1)² = ¹/(4-Y) (b) Find the XY- and xy-coordinates of the vertex and focus. vertex focus XY-coordinates xy-coordinates Need Help? X (x, y) = Read It (x, y) = 65√2 16 (c) Find the equation of the directrix in XY- and xy-coordinates. 65√2 16 XY-coordinates 1,- 4 1, -63 16 (x, y) = = (x, y) xy-coordinates 5√2 2 79√2 32 9 2 3√2 2 47√2 32
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