Question

find the equation of circle whose two diameters are y=2x and x+y=6 and perimeter is 6π ?
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Answer 1

Answer:

Two diameters are the lines,

x+y=4 ----- ( 1 )

x−y=2 ----- ( 2 )

So, first, we find the intersection point of diameters that is the center of the circle.

Adding equation ( 1 ) and ( 2 ) we get,

⇒ 2x=6

⇒ x=3

Substituting value of x in equation ( 1 ),

⇒ 3+y=4

⇒ y=1

So, the center of circle is (3,1).

Now, circle is pass through (4,6)

The equation of circle is (x−a)

2

+(y−b)=r

2

, where (a,b) co-ordinates of circle and r is radius.

Put center coordinates and pass through point

⇒ (4−3)

2

+(6−1)

2

=r

2

⇒ 1+25=r

2

⇒ r

2

=26

So, the equation of circle is,

⇒ (x−3)

2

+(y−1)

2

=26

⇒ x

2

−6x+9+y

2

−2y+1=26

⇒ x

2

+y

2

−6x−2y−16=0