Question

find the equation of a circle concentric with the circle 2x²+2y²–6x+8y–1=0 and double of its area

Answer 1

Answer:

Center of the given circle

x

2

+y

2

−3x+4y+

2

1

=0

is (

2

3

,−2)

Area of the given cirle =πr

1

2

Area of circle to be found =2πr

1

2

⇒r

2

=

2

r

1

g

2

=g

1

=

2

−3

f

2

=f

1

=2

r

1

=

g

1

2

+f

1

2

−c

=

4

9

+4−

2

1

4

9+16−2

=

4

23

r

2

=

2

23

and r

2

=

g

2

2

+f

2

2

−c

2

=

4

9

+4−c

2

=

2

23

⇒

4

25

−c

2

=

2

23

⇒c

2

=

4

25

−

2

23

=

4

−21

∴ Equation of required circle:

x

2

+y

2

−3x+4y−

4

21

=0

⇒4x

2

+4y

2

−12x+16y−21=0