Let P(x1, y1) 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 B be the angle between the vertical line r = x1 and the parabola. %3D (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 L1 and L2, respectively, then it is known that m2 – mị 1+ mịm2 tan e = (b) By using the fact given above, show that a = B.
Let P(x1, y1) 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 B be the angle between the vertical line r = x1 and the parabola. %3D (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 L1 and L2, respectively, then it is known that m2 – mị 1+ mịm2 tan e = (b) By using the fact given above, show that a = B.
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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Transcribed Image Text:Let P(x1, 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 B be the angle
between the vertical line x = x1 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
L1 and L2, respectively, then it is known that
m2 – mị
tan 0 =
1+ mịm2
(b) By using the fact given above, show that a =
— В.
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