So I have a question saying, "Find the smallest value of $$ x^2 + y^2 -2x + 6y + 3= 0." $$ I know how to make this into a circle equation $$(x-1)^2 + (y+3)^2 =7$$ (if I'm not wrong) and graph it, but where and how do I find the smallest value on this circle?
any answers appreciated :)
I presume you are talking about the modulus of x and y coordinates. As the modulus of a point increases with radial distance from the origin we construct a line joining origin and centre of circle and find the point of intersection of the circle with this line. which gives the point of intersection as 0.163 i - o.49 j which is the minimum value of the modulus of a point lying on the circle.