Question

x=-2/3,y=1/-6 ?

x= minus 2 by 3 comma y= 1 by minus 6 ?​

Answer 1

Answer:

Step-by-step explanation:

x

2

+y

2

+2gx+2fy+c=0        .....(1)

where (−g,−f) is center and g

2

+f

2

−c is the radius.

Since, the circle passes through (2,3), so it satisfies eqn (1)

⇒4+9+4g+6f+c=0

⇒4g+6f+c=−13      .....(2)

Since, the circle passes through (−1,1), so it satisfies eqn (1)

⇒1+1−2g+2f+c=0

⇒−2g+2f+c=−2      .....(3)

Subtracting eqn (3) from eqn (2), we get

6g+4f=−11       ....(4)

Given center lies on the line x−3y−11=0

Since, center (−g,−f) satisfies this equation.

⇒−g+3f=11        ....(5)

Solving eqn (4) and (5), we get

g=

2

−7

​

,f=

2

5

​

Put this value in (2), we get

c=−14

Substituting these values in (1),

x

2

+y

2

−7x+5y−14=0