Need help with geometry (circles)?

Question

Find the equation of a circle with centre (2,5) which touches the x axis.

Answer 1

Circle Centre coordinates ( h , k ) = ( 2 , 5 )

Circle is touching the x axis.

So radius r = ( x-coordinate of Centre of circle )

r = 2

General form of Circle equation : ( x - h )² + ( y - k )² = r²

Substitute h = 2 , k = 5 , r = 2

( x - 2 )² + ( y - 5 )² = 2²

x ² - 4x + 4 + y² - 10x + 25 = 4

x ² + y² - 4x - 10y + 25 = 0

Required circle equation is x ² + y² - 4x - 10y + 25 = 0