Math, asked by mohammednouman624, 6 months ago

find the equation of the circle passing through the following 3 points (3,4) (3,2) and (1,4)​

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Answered by ghatejanhavi74
3

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Find the equation of the circle passing through the points (3,4),(3,2) and (1,4)

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ANSWER

Let the equation of circle be-

x

2

+y

2

+2gx+2fy+c=0.....(1)

Given that the circle passes through the points (3,4),(3,2) and (1,4).

Therefore,

(3)

2

+(4)

2

+2g(3)+2f(4)+c=0

⇒9+16+6g+8f+c=0

⇒6g+8f+c+25=0.....(2)

(3)

2

+(2)

2

+2g(3)+2f(1)+c=0

⇒9+4+6g+2f+c=0

⇒6g+2f+c+13=0.....(3)

(1)

2

+(4)

2

+2g(1)+2f(4)+c=0

⇒1+16+2g+8f+c=0

⇒2g+8f+c+17=0.....(4)

Subtracting equation (3) from (2), we have

(6g+8f+c+25)−(6g+2f+c+13)=0

6g+8f+c+25−6g−2f−c−13=0

⇒f=

6

−12

=−2

Now subtracting equation (4) from (2), we have

(6g+8f+c+25)−(2g+8f+c+17)=0

6g+8f+c+25−2g−8f−c−17=0

⇒g=

6

−8

=

3

−4

Now substituting the value of g and f in equation (2), we have

6(

3

−4

)+8(−2)+c+25=0

−8−16+c+25=0

⇒c=−1

Substituting the values of g,f and c in equation (1),

we get

x

2

+y

2

+2(

3

−4

)x+2(−2)y+(−1)=0

x

2

+y

2

3

8

x−4y−1=0

Hence the equation of circle passing through the given points is x

2

+y

2

3

8

x−4y−1=0.

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