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(d) Write equations for the directrix and axis of symmetry.

(d) Write equations for the directrix and axis of symmetry.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section: Chapter Questions
Problem 7DE
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For the equation of the parabola given in the form x² =4py, (a) Identify the vertex, value of p, focus, and focal diameter of the parabola. (b) Identify the endpoints of the latus rectum. (c) Graph the parabola. (d) Write equations for the directrix and axis of symmetry. Express numbers in exact, simplest form. 2x² = 18y Part: 0 / 4 Part 1 of 4 (a) The vertex is The focus is 00. 0.0. The focal diameter is unit(s).
Transcribed Image Text:For the equation of the parabola given in the form x² =4py, (a) Identify the vertex, value of p, focus, and focal diameter of the parabola. (b) Identify the endpoints of the latus rectum. (c) Graph the parabola. (d) Write equations for the directrix and axis of symmetry. Express numbers in exact, simplest form. 2x² = 18y Part: 0 / 4 Part 1 of 4 (a) The vertex is The focus is 00. 0.0. The focal diameter is unit(s).
Step 2: Solving part a a.)2x² = 18y: ⇒ 2x² = 18y ⇒2(x-h)² =18(y-k) 18(y-k) ⇒ (x-h)² 2 ⇒(x-h)² =9(y-k) Upon comparing with (x-h)² = 4p(y-k), we get: Vertex, (h,k)= (0,0) Finding p: ⇒4p=9 ⇒p: Focus = (0,p) = - (0.p)-(0.²) Finding focal diameter of the parabola: ⇒ L=4p ⇒ L=4 9 4 ⇒L=9 SO, Focal diameter = 9units Step 3: Solving part b b.) Finding endpoints of latus rectum: ⇒ (2p,p),(2p.p) → SO, Endpoints of latus rectum are = 10 c.)Graph of the parabola is given by: 99 Step 4: Solving part c -8 and -6 9 2-3) V (0, 2.25) (-4.5, 2.25) -2 (0,0) (4.5, 2.25) 6
Transcribed Image Text:Step 2: Solving part a a.)2x² = 18y: ⇒ 2x² = 18y ⇒2(x-h)² =18(y-k) 18(y-k) ⇒ (x-h)² 2 ⇒(x-h)² =9(y-k) Upon comparing with (x-h)² = 4p(y-k), we get: Vertex, (h,k)= (0,0) Finding p: ⇒4p=9 ⇒p: Focus = (0,p) = - (0.p)-(0.²) Finding focal diameter of the parabola: ⇒ L=4p ⇒ L=4 9 4 ⇒L=9 SO, Focal diameter = 9units Step 3: Solving part b b.) Finding endpoints of latus rectum: ⇒ (2p,p),(2p.p) → SO, Endpoints of latus rectum are = 10 c.)Graph of the parabola is given by: 99 Step 4: Solving part c -8 and -6 9 2-3) V (0, 2.25) (-4.5, 2.25) -2 (0,0) (4.5, 2.25) 6
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