Unit 1 – Conic Sections Section 1.3 – The Parabola Calculator Required Vertex: (h, k) Opens...
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Transcript of Unit 1 – Conic Sections Section 1.3 – The Parabola Calculator Required Vertex: (h, k) Opens...
Unit 1 – Conic SectionsSection 1.3 – The Parabola
Calculator Required
2y 4k hxp 2
x 4h kyp
Vertex: (h, k)
Opens Left/Right Opens Up/Down
Vertex: (h, k)
Focus: h kp, Focus: h, k p
Directrix: x ph Directrix: y pk
Axis of Sym: y k Axis of Sym: x h
V
p
2p2pF
p
Directrix
Vp
2p
2p
Fp
Directrix
Given the equation 2x 8ya) Write the equation in standard form
2x 4h kyp 2
x y0 024
V
F
b) Provide the appropriate information.
Focus: (0, 2)Vertex: (0, 0)
Directrix: y = -2Axis of Sym: x = 0
c) Graph the equation
Given the equation 2y 8x 4y 20 0 a) Write the equation in standard form
2y 4y 8x 20 2 4 4y 4y 8x 20
2y 82 x 16
22x2y 8
2y 42 2x2
Given the equation 2y 8x 4y 20 0 a) Write the equation in standard form
2y 4y 8x 20 2y x2 224
V
F
b) Provide the appropriate information.
Focus: (4, 2)Vertex: (2, 2)
Directrix: x = 0Axis of Sym: y = 2
c) Graph the equation
Given the equation 2x 6x 8y 7 0 a) Write the equation in standard form
2x 6x 8y 7 2 9 9x 6x 8y 7
2y 63x 8 1
2283x y
2x 43 y2 2
Given the equation 2x 6x 8y 7 0 a) Write the equation in standard form
2x 6x 8y 7 0 2x 43 2y2
V
F
b) Provide the appropriate information.
Focus: (3, 0)Vertex: (3, 2)
Directrix: y = 4Axis of Sym: x = 3
c) Graph the equation
Write the equation of the parabola with focus at (2, 2)and directrix x = 4
F
V
2y 4k hxp
2y 42 x1 3
242 3y x
Write the equation of the parabola with V(-1, -3) and F(-1, -6)
V
F
2x 4h kyp
2x 4 31 3y
221 3x y1