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1. Find the Equation of a Parabola that has its vertex at the origin and satisfies the following conditions: (a) Focus: F(5,0) (b) Directrix: y=-5 (c) Directrix has x-intercept 5

1. Find the Equation of a Parabola that has its vertex at the origin and satisfies the following conditions: (a) Focus: F(5,0) (b) Directrix: y=-5 (c) Directrix has x-intercept 5

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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**Problem:** Find the equation of a parabola that has its vertex at the origin and satisfies the following conditions: (a) Focus: F(5, 0) (b) Directrix: y = -5 (c) Directrix has x-intercept 5 **Explanation:** This problem asks for the equation of a parabola with specific characteristics. The vertex is at the origin (0,0), and the focus is at point F(5,0), indicating the parabola opens horizontally. The directrix is given as y = -5; however, the mention of an x-intercept being 5 suggests checking for consistency in problem constraints. **Additional Notes:** - The typical equation format for a parabola with a horizontal axis of symmetry (opening right or left) is \( x = ay^2 + by + c \). - Focus and directrix properties can be used to find the correct value of the parameter(s) determining the parabola's opening and orientation.
Transcribed Image Text:**Problem:** Find the equation of a parabola that has its vertex at the origin and satisfies the following conditions: (a) Focus: F(5, 0) (b) Directrix: y = -5 (c) Directrix has x-intercept 5 **Explanation:** This problem asks for the equation of a parabola with specific characteristics. The vertex is at the origin (0,0), and the focus is at point F(5,0), indicating the parabola opens horizontally. The directrix is given as y = -5; however, the mention of an x-intercept being 5 suggests checking for consistency in problem constraints. **Additional Notes:** - The typical equation format for a parabola with a horizontal axis of symmetry (opening right or left) is \( x = ay^2 + by + c \). - Focus and directrix properties can be used to find the correct value of the parameter(s) determining the parabola's opening and orientation.
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