How do use the method of translation of axes to sketch the curve #x^2+y^2-4x+3=0#?
1 Answer
Jan 6, 2018
We have a conic:
# x^2+y^2-4x+3 = 0 #
We rearrange and complete the square of the
# (x^2-4x) +(y^2) + 3 = 0 #
# :. (x-2)^2-(2)^2 + y^2 + 3 = 0 #
# :. (x-2)^2-4 + y^2 + 3 = 0 #
# :. (x-2)^2 + y^2 = 1 #
Comparing with:
# (x-a)^2+(y-b)^2 = r^2 #
We see that the conic is a circle of radius
Alternatively, if we compare to the origin centred circle
So the graph is as follows:
graph{x^2+y^2-4x+3 = 0 [-3.656, 6.344, -2.5, 2.5]}