Let Cr x y R times R x2 y2 r2 where r R Findr Cr andr Cr

Let C_r = {(x, y) R times R | x^2 + y^2 = r^2} where r R^+. Find_r C_r and_r C_r. Prove your answer.

C_r represents the circle in the xy plane with centre at the origin and radius =r.

Since r belongs to r+, r cannot be negative

Intersection of all circles with radius in R+ will be the circle common to the family of circle with centre at origin.

Hence will be the point (0,0)

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Union of all circles will be the biggest circle in the xy plane with the radius r nearing infinity and centre at (0,0)

So union will be the full xy plane.

$Let C_r = {(x, y) R times R | x^2 + y^2 = r^2} where r R^+. Find_r C_r and_r C_r. Prove your answer.SolutionCr represents the circle in the xy plane with centr$

Let Cr x y R times R x2 y2 r2 where r R Findr Cr andr Cr

Solution

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