*(1)(a) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z):...

*(1)(a) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): z=c}.

(b) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): x=a}.

(c) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): y=b}.

*(2) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): z=kx+b} assuming both b and k are positive.

(a) For what value of k is this an hyperbola and for what value of k is this an ellipse?

(b) Plot one of each.

Justify your answer.

Expert Solution

Colby Messinger answered 1 year ago

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