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

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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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