1. The equation of a circle is x^2 - 10x + y^2 + 8y - 8 = 0. What are the center and the radius of the circle?
2. Write the equation of the cirlce in general form.
3. Write the equation of a parabola shown in the picture.
+6248 1) \(x^2 - 10x + y^2 + 8y -8 = 0\\ (x^2 - 10x +25 - 25)+ (y^2 +8y + 16-16)-8=0\\ (x-5)^2 - 25 + (y+4)^2-16 - 8 = 0\\ (x-5)^2+ (y+4)^2 = 49= 7^2\\ C=(5,-4),~r=7\)
2) \(\text{The center is at }(-2,3)\\ \text{The radius is }3\\ (x+2)^2 +(y-3)^2 = 9\)
3) \(\text{Vertex at }(2,3)\\ f(x) = a(x-2)^2+3\\ (0,4) \text{ on the parabola}\\ 4a+3=4\\ a=\dfrac 1 4\\ f(x) = \dfrac 1 4 (x-2)^2+3\)
