Question

The radius of the circle whose equation is given parametrically as x = 3sinθ – 4cosθ and y = 3cosθ + 4sinθ, θ ∈ R is equal to ??

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Answer 1

Answer:

The radius of the circle whose equation is given parametrically as x = 3sinθ – 4cosθ and y = 3cosθ + 4sinθ, θ ∈ R is equal to ??

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Answer 2

Answer:

Given x=−3+4cosθ⇒x+3=4cosθ⇒

4

x+3

=cosθ.....(1)

y=4+4sinθ⇒y−4=4sinθ⇒

4

y−4

=sinθ.....(2)

Squaring equation (1) and (2) and adding them,

(

4

x+3

)

2

+(

4

y−4

)

2

=sin

2

θ+cos

2

θ⇒

4

2

(x+3)

2

+(y−4)

2

=1⇒x

2

+9+6x+y

2

+16−8y=16

⇒x

2

+y

2

+6x−8y+9=0 is the required equation of the circle