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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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