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# MTH201 Multivariable Calculus Assignment No 02 Solution & Discussion Due Date: 17-07-2014

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Our main purpose here discussion not just Solution

We are here with you hands in hands to facilitate your learning and do not appreciate the idea of copying or replicating solutions.

QUESTION NO. 2

SOLUTION:

1) Symmetry about the Initial Line

If the equation of a curve remains unchanged when (r,θ)
is replaced by either (r,-θ) in its equation ,then the curve

If when (r, θ) is replaced by either (r,π θ − ) in
The equation of a curve and an equivalent equation
is obtained ,then the curve is symmetric about the
line perpendicular to the initial i.e, the y-axis

If the equation of a curve remains unchanged

when either (-r, θ) or is substituted for (r, θ)
in its equation ,then the curve is symmetric
about the pole. In such a case ,the center of
the curve.

Equation of the curve in polar co-ordinates is r2=-4sin2θ

(i) Symmetry about the Initial Line.
r2=-4sin2θ
Remember that sine is an odd function
Put (r,-θ) in equation
r2=-4sin2 (-θ)
r2=-4sin (-2θ)
r2=4sin2θ
This equation is not symmetry about initial line
r2=-4sin2θ
Put (-r, θ) in equation
(-r) 2 =-4sin2θ
r2=-4sin2θ
This equation is symmetry about pole

Q:1:- Equation of the curve in polar co-ordinates is =-4sin2 discuss the symmetry of graph of this curve about.
Initial line
Pole

Equation of the curve in polar co-ordinates is
=-4sin2θ
=-4sin2θ
sin is odd function.
Put (r, -θ) in equation
=-4sin2 (-θ)
=-4sin (-2θ)
=4sin2θ
this equation is not symmetry about initial line
=-4sin2θ
Put (-r, θ) in equation
=-4sin2θ
=-4sin2θ
This equation is symmetry about pole

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