SOLUTION: Find the equation of a circle passing through two points (-4,1) and (4,5) whose centre lies on the straight line 2x-y=1

Question 1106619: Find the equation of a circle passing through two points (-4,1) and (4,5) whose centre lies on the straight line 2x-y=1
Answer by dkppathak(439) (Show Source): You can put this solution on YOUR website!
Find the equation of a circle passing through two points (-4,1) and (4,5) whose centre lies on the straight line 2x-y=1
(X-h)^2 +(y-k)^2=r^2
the circle passing through -4,1
(-4-h)^2 +(1-k)^2=r^2 ---(1)
the circle passing through 4,5
(4-h)^2 +(5-k)^2=r^2 ---(2) 1 and 2 both are equal
(-4-h)^2 +(1-k)^2 =(4-h)^2 +(5-k)^2
16+h^2+8h+1+k^2-2k=16+h^2-8h+25+k^2-10k
16h+8k-24=0
2h+k=3 (3)
center lies on line 2x-y=1 center h,k lies and satisfy the line
2h-k=1 (4) by solving 3, 4 we will get h=1 and k=1
by putting the value of h and k in equation 1 we will get radius =5
equation of circle will bw
(x-1)^2 +(y-1)^2=25
or
x^2+y^2-2x-2y-23=0

RELATED QUESTIONS
Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose... (answered by fcabanski)

Find the equation of the circle whose centre lies on the line y=4 and which passes... (answered by Alan3354)

Please help me solve this problems: 1.A circle whose centre lies on the line y=3x-1,... (answered by Alan3354)

Find the equation of the circle which passes through points (2,-2) and (3,4) and whose... (answered by ikleyn,Alan3354)

Find the equation of a circle centre on the line y=2x+1 touching the y axis and passing... (answered by Alan3354)

Points A(2, 1) and B (4, -5) like on a circle. If line 2x-y-13=0 is a tangent to the... (answered by josgarithmetic,MathTherapy)

A circle touches the positive x and y axis, it's centre lies on the line y= 3x minus... (answered by Alan3354)

A circle whose centre lies on the line y=3x-1, touches both axes. Find the equation of... (answered by ikleyn)

Find the equation of the line passing through the points ( - 4, 8) and (5, -1). Also... (answered by checkley77)