Question

If the coordinates of the end points of a circle are A(1,2) B(5,6) then find the coordinate of the center of the circle​

Answer 1

Answer:

Hii,

Step-by-step explanation:

Let,

A(x1 , y1) = (1.2)

B(x2, y2) = (5,6)

centre of the circle be,

O(x,y)

since, points A & B lies on the same circle

thus, distance between point & centre will be the radius & will be equal for the both

=> AO = BO

squaring both sides,

=> AO² = BO²

therefore, by distance formula,

=> (x-x1)² + (y-y1)² = (x-x2)² + (y-y2)²

=> (x-1)² + (y - 2)² = (x-5)² + (y-6)²

=> (x² + 1 - 2x) + (y² + 4 - 4y) = (x² + 25 - 10x) + (y² + 36 - 12y)

=> -2x -4y +5 = -10x -12y + 61

=> 10x - 2x + 12y - 4y - 61 + 5 = 0

=> 8x + 8y + 56 = 0

=> 8 ( x + y + 7) = 0

=> x + y = -7

similarly,...

Thank you!