Soru 4 10 puan Which one of the following describes the intersection of surfaces z2=x2+y2 and...

Question

Question

Soru 4 10 puan Which one of the following describes the intersection of surfaces z2=x2+y2 and z2+x2+y2=1? Circle Ellipse O Li

math geometry

Answer 1

Answer #1

Given, equation two surface are

z^2 = x^2 + y^2 ----------------(1)

and z^2 + x^2 + y^2 =1 --------------(2)

Now, eliminating z^2 from (1) and (2) we get,

(x^2 + y^2) + ( x^2 + y^2) = 1

Or, 2(x^2 + y^2) = 1

Or, x^2 + y^2 =1/2

Or, x^2 + y^2 = (1/√2)^2.

This is equation of a circle .

Hence, intersection of two given surface is a circle.

Ans------->1st option.

Answer 2

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