Question

find the equation of the circle which passes through the points (4,1) (6,5) and has its centers on the line 4x+y=16

Answer 1

Let the center be (h,k).
Since, center lies on 4x+y=16...........(1),
Substitute point (h,k) in above eqn 1
You will get a relation between h and k
4h+k=16
or, k=4h-16

Now find distances from center (h,k) to given two points, they will be equal since both are radius.. Solve further, you will get values of center (h,k)
And then calculate radius..

With those information, you will finally get equation of circle..

Answer 2

how about this formula x^2+y^2+2gx+2fy+c=c

Answer 3

=0 i mean

Answer 4

yeah you can also solve by this method..
(h,k)=(-g,-f)
or, (h, 4h-16)=(-g,-f)
substitute the points, you will get two variables and two equations. solve them..
You can do it..

Answer 5

i have no idea how to do this can u xplain every step pls?

Answer 6

I am not going to do everything for you.. put g=-h
f=-(4h-16)
And substituting two points on circle in that standard equation gives you two equations.. with two variables h and c.. solve them find h and c. from h determine g and f.. Now you will have all f,g,c. So, you will have the equation of circle..