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For the equation of the parabola given in the form (x-h)² = 4p(y-k). (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. (x-3)²=-12(y+4)

For the equation of the parabola given in the form (x-h)² = 4p(y-k). (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. (x-3)²=-12(y+4)

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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Question
For the equation of the parabola given in the form (x-h)² = 4p(y-k). (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. (x − 3)² = − 12 (y+4) Part 1 of 4 (a) The vertex is The focus is ( The focal diameter is ■>. unit(s). X
Transcribed Image Text:For the equation of the parabola given in the form (x-h)² = 4p(y-k). (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. (x − 3)² = − 12 (y+4) Part 1 of 4 (a) The vertex is The focus is ( The focal diameter is ■>. unit(s). X
Expert Solution
Step 1

Note: As per the honor code, only one question can be solved at a time and up to 3 sub-parts only. Please post other sub-parts separately.

Given- The parabola: x - 32 = -12y + 4

To find- 

  1. The vertex, value of p, focus, and focal diameter of the parabola.
  2. Identify the endpoints of the latus rectum.
  3. Graph the parabola.

 

Concept used- 

The Standard form of parabola with Vertex h, k is given by

x - h2 = 4py - k

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