# On a single set of axes, sketch a picture of the graphs of the following four...

###### Question: On a single set of axes, sketch a picture of the graphs of the following four equations: y = -x + V2. y = -x - v2, y = x + V2, and y = x-V2. These equations determine lines, which in turn bound a diemand Sheped region in the plane. (a) At how many points does the line y = -x + 2 intersect the unit circle? At how many points does the line y = -x-vī intersect the unit circle? At how many points does the line y=x+intersect the unit circle? 1 At how many points does the line y = x - intersect the unit circle? 1 1 (b) Find the intersection points between the unit circle and each of the four lines. (Order your answers from smallest to largest x, then from smallest to largest y.) Vai-VE) (x,y) - ha va V2 (X,Y)= (-) Viva (c) Construct a diamond shaped region in which the dircle of radius 1 centered at (-2,-5) sits tangentially. Use the techniques of this section to help. (Order your answers from smallest to largest slope, then from smallest to largesty Intercept. Use x as your variable.) y = -x+ 2 X y = (x+2) - V - 5 x y = -(x+2) - V2 X

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