Question

Find the equation to the cone with the
vertex at the origin and whose guiding
curve is given by x2+y2=9, z=3.
(A) x² - y2 - 22 = 0
(B)
x2 + y2 - 22 = 0
(C) x3 + y3 - 2 = 0
(D) None of the above​

Answer 1

Answer:

What will be the equation of the cone whose vertex is (1,2,3)(1,2,3) and guidelines curve the circle x2+y2+z2=4x2+y2+z2=4 and x+y+z=1x+y+z=1?

Let S(p,q,r) be a point on the guide line curve.

Thenp2+q2+r2=4p2+q2+r2=4(1)

and p+q+r=1p+q+r=1 (2)

The line joining S and Vertex V=(1,2,3)V=(1,2,3)is given by

x−1p−1=y−2q−2=z−3r−3=kx−1p−1=y−2q−2=z−3r−3=k

k=x−1+y−2+z−3p−1+q−2+r−3=x+y+z−6p+q+r−6=x+y+z−6−5

Answer 2

Answer:

as the equation of the cone will be homogeneous of degree 2 because it has its vertex at origin

x^2+y^2=9z^2