Question

Find the parametric equation of the circle x*+y*-6x+4y-3=0​

Answer 1

Step-by-step explanation:

Given equation of circle is x

2

+y

2

−6x+4y−12=0

⟹x

2

−6x+y

2

+4y−12=0

⟹x

2

−2(x)(3)+(3)

2

−(3)

2

+y

2

+2(y)(2)+(2)

2

−(2)

2

−12=0

⟹(x−3)

2

−9+(y+2)

2

−4−12=0

⟹(x−3)

2

+(y+2)

2

=5

2

Let X=x−3,Y=y+2

⟹X

2

+Y

2

=5

2

This is in the form of x

2

+y

2

=a

2

which as parametric equations as x=acosθ,y=asinθ

⟹X=5cosθ,Y=5sinθ

⟹x−3=5cosθ,y+2=5sinθ

⟹x=3+5cosθ,y=−2+5sinθ