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1. Let P(r1, yı) be a point on the parabola r = 4py, p > 0, with focus F(0, p). Let a be the angle between the parabola and the line segment FP, and let 3 be the angle between the vertical line r = 1, and the parabola. (a) Determine an equation of the tangent line of the parabola at point P.

1. Let P(r1, yı) be a point on the parabola r = 4py, p > 0, with focus F(0, p). Let a be the angle between the parabola and the line segment FP, and let 3 be the angle between the vertical line r = 1, and the parabola. (a) Determine an equation of the tangent line of the parabola at point P.

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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1. Let P(r1, y1) be a point on the parabola x? = 4py, p> 0, with focus F(0, p). Let a be the angle between the parabola and the line segment FP, and let 3 be the angle between the vertical line r = , and the parabola. (a) Determine an equation of the tangent line of the parabola at point P. Given two lines L1 and L2 intersecting at an angle 0, if m1 and m2 are the slopes of L, and L2, respectively, then it is known that m2 - mị tan 0 = 1+ mim2 (b) By using the fact given above, show that a = B.
Transcribed Image Text:1. Let P(r1, y1) be a point on the parabola x? = 4py, p> 0, with focus F(0, p). Let a be the angle between the parabola and the line segment FP, and let 3 be the angle between the vertical line r = , and the parabola. (a) Determine an equation of the tangent line of the parabola at point P. Given two lines L1 and L2 intersecting at an angle 0, if m1 and m2 are the slopes of L, and L2, respectively, then it is known that m2 - mị tan 0 = 1+ mim2 (b) By using the fact given above, show that a = B.
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