A circle of radius 10 units is drawn with (8,6) as the centre. At which of the given points does the circle pass through the co-ordinate axes?
Given the radius of the circle is 10 units. and the centre is (8,6).
Let a point 'P' on the circle be (x,y).
(∵ distance from centre to any point on circle is equal to its radius)
To find coordinates where circle passes through Y-axis put x =0 in eq (1)
(∵ X-coordinates of any point on y-axis is O)
⇒y−6=6 (or) y−6=−6
⇒y=12 (or) y=0
∴ Points where circle passes through Y-axis are (0,12) and (0,0)
To find X-intercept put y =0
⇒x−8=8 (or) x−8=−8
⇒x=16 (or) x=0
∴ Points where circle passes through X-axis are (16,0) and (0,0)