Answer:
option 3
Explanation:
we know the equation of a circle follows the form of:
and we also know that the centre point is (-f,-g)
From this information we can simply figure which of the equations will give us the centre point of (2,1) (x,y)
In the equation of a circle, we notice that the f and g value is multiplied by 2 (i.e 2fx, 2gy) , hence in order to find the f and g value from the options we must divide by 2.
1) In the first option, finding the f value:
2fx = -4x
2f = -4
f = -4/2
f = -2
finding the g value:
2gy = -6y
2g = -6
g = -6/2
g= - 3
hence the centre point of this equation would be:
(2, 3) which is (-f,-g) therefore it's incorrect.
now instead of doing this for all the other options as it will be time consuming, we know that from in the previous option it had the correct f value but wrong g value so we can just look for a similar equation.
2) Only in option 3 we notice that the 2fx value will be the same and simply we can just just to be certain the g value will also be correct.
finding the g value:
2gy = -2y
2g = -2
g = -2/2
g = -1
and now we just change the signs because the centre point follows (-f, -g) hence the centre point of option 3 is (2, 1) which is the correct answer
And also there was no need to act on the additional information the question had given about the line the equation had touch.