As shown in figure below, in Cartesian coordinate system rOy, there is a line i: I-y-2 0 and a parabola C : y = 2pr(p>0). (1) If line / passes the focus of parabola C, what is the equation of parabola C? (2) There are two points P.Q on C such that P and Q are symmetric with respect to line I. a. Prove that the midpoint of line segment PQ is (2 – p.-p). b. What is the range of possible values of p?

As shown in figure below, in Cartesian coordinate system rOy, there is a line i: I-y-2 0 and a parabola C : y = 2pr(p>0). (1) If line / passes the focus of parabola C, what is the equation of parabola C? (2) There are two points P.Q on C such that P and Q are symmetric with respect to line I. a. Prove that the midpoint of line segment PQ is (2 – p.-p). b. What is the range of possible values of p?

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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Concept explainers

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

As shown in figure below, in Cartesian coordinate system rOy, there is a line I:
I-y-2 =0 and a parabola C : y = 2pr(p>0).
(1) If line / passes the focus of parabola C, what is the equation of parabola C?
(2) There are two points P.Q on C such that P and Q are symmetric with respect to
line 1.
a. Prove that the midpoint of line segment PQ is (2 - p.-p).
b. What is the range of possible values of p?
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