Question

f the equation of a circle is (x - 2)2 + (y - 6)2 = 4, it passes through point ______. (2, 8) (5, 6) (-5, 6) (2, -8)

Answer 1

(2, 8).

Explanation:

(x - 2)^2 + (y - 6)^2 = 4

If x = 2 and y = 8 we have:

(2 - 2)^2 + (8 - 6)^2

= 0 + (2^2

= 4.

So it passes through the point (2,8).

Answer 2

The point through which the circle passes is:

(2,8)

Explanation:

The equation of the circle is given by:

`(x-2)^2+(y-6)^2=4`

We will check by putting each point in the equation and check which is equal to 4.

1)

(2,8)

when x=2 and y=8 we have:

`(2-2)^2+(8-6)^2=4\\\\i.e.\\\\0^2+2^2=4\\\\i.e.\\\\4=4`

Hence, the circle passes through the point (2,8).

2)

(5,6)

when x=5 and y=6 we have:

`(5-2)^2+(6-6)^2=4\\\\i.e.\\\\3^2+0^2=4\\\\i.e.\\\\9=4`

which is not true.

Hence, the circle does not pass through (5,6).

3)

(-5,6)

when x= -5 and y=6 we have:

`(-5-2)^2+(6-6)^2=4\\\\i.e.\\\\(-7)^2+0^2=4\\\\i.e.\\\\49=4`

which is not true.

Hence, the circle does not pass through (-5,6).

4)

(2,-8)

when x=2 and y= -8 we have:

`(2-2)^2+(-8-6)^2=4\\\\i.e.\\\\0^2+(-14)^2=4\\\\i.e.\\\\196=4`

Hence, the circle does not passes through the point (2,-8).