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Problem Solving (PS) | Re: If x^2+y^2=1 and ||x|-0.34|+0.66=y, how many values can x take?

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We just need to figure out whether point of minima of ||x|-0.34|+0.66=y lies within the circle or not, and whether local maxima at x=0 lies within circle or not.
x2+y2=1x2+y2=1 is a curve of a circle of radius 1.

At x=0, ||x|-0.34|+0.66= 1, which lies on the circle.

Minima of ||x|−0.34|+0.66=y||x|−0.34|+0.66=y occurs when |x|-0.34=0 or x=+0.34 and -0.34, and y=0.66, lie inside the circle.

Now we are good to draw the curve.

There are 3 points where both curves meet.

D

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