Question

Find the equation of the circle passing through the intersection of the circlesandand the point (3,4)

1) 

2) 

3)

4) 

Comments

We need at least 3 passing points to determine the equation of a circle. One passing point is already given. Solve the given two equation of circles to find the remaining two passing points and hence find the equation of the required circle.

Answer 1

The set  of circles passing through the two points of intersection is

(x-5)^2+y^2-25-k[x^2+(y-5)^2-25]=0,where k is parameter.

As the circle passes through (3,4) we can write

(3-5)^2+4^2-25-k[(3^2+(4-5)^^2-25]=0

=>4+16-25-k(9+1-25)=0

=>-5+15k=0

=>k=1/3

So the required equation of  the circle

(x-5)^2+y^2-25-1/3[x^2+(y-5)^2-25]=0

=>3x^2-30x+75-75+3y^2-x^2-y^2+10y-25+25=0

=>2x^2+2y^2-30x+10y=0

=>x^2+y^2-15x+5y=0

=>(x-15/2)^2+(y+5/2)^2=125/2

So option will be (4)None

Comments

please solve with the help of options

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Is it OK now?

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sorry bro but answer given is option (c)

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Figure supports my answer.