The equation of a circle, C, is x^2 +y^2 - 2x -6y +1 =0
Find the equation of the circle which is a reflection of C in the y-axis.
In the earlier part, I was told to find the coordinates of the centre of circle and its radius. The answers are (1,3) and 3 units respectively.
Going on to part 2 of the question, since reflection is about the y- axis, well, shouldn't the x-coordinate of the reflected circle be -3 (since 0 to -3 is 3 units) and the y-coordinate still remain as 3?
However the answer given is x^2 +y^2 + 2x -6y +1 =0
So totally different from my answer when i expand it out! lol
When u do a flip on the y axis, only x changes from positive to negative or negative to positive. The only effect it has on the equation will be the -2x term which becomes a +2x term. The y are not changed and there is no change to x^2 since the value is the same regardless whether x is positive or negative.
If (1,3) is the center of the circle and the radius is 3 units, this means the circle stretch from -2 to 4, on reflection, you get -4 to 2 and the center of the circle becomes (-1,3). What made you think of -3?
Originally posted by limywv:Now A maths teaching circles already?
You will be surprised how much stuff was moved down from JC-lvl to A. Maths-lvl.