Question

Find equation of circle passing through point 7,3 with radius 3 units and whose center lies on line x-y-1=0

Answer 1

Answer:

(x - 4)² + (y - 3)² = 3² or

(x - 7)² + (y - 6)² = 3²

Step-by-step explanation:

Hi,

Given that the circle passes through point A(7, 3).

Given the radius of the circle , r = 3

Also, given the center of the circle lies on line x - y - 1  = 0

=> Center will be of the form O(h, h - 1).

But distance of point A from O center of circle should be equal to radius,

=> OA = 3

=> OA² = 9

=> (h - 7)² + (h - 1 - 3)² = 9

=> (h - 7)² + (h - 4)² = 9

=> h² - 14h + 49 + h² - 8h + 16 = 9

=>2h² - 22h + 56 = 0

=>h² - 11h + 28 = 0

=> h = 4 or 7

=> Possible center's of circle are (4, 3) or (7, 6)

So, equation of circles would be

(x - 4)² + (y - 3)² = 3² or

(x - 7)² + (y - 6)² = 3²

Hope, it helped !