Answer to Question #278630 in Analytic Geometry for Nofiu pelumi

Question #278630

Find an equation of the sphere with center c that is tangent to (a) the xy-plane, (b) the xz- plane and (c) the yz-plane


(i)C(-2,4,-6)


1
Expert's answer
2021-12-14T14:23:16-0500

(a)

Since the sphere touches the xy-plane, its radius is the distance from its center, "(-2, 4, -6)," to the xy-plane, which is "6." Therefore "r = 6" and an equation of the sphere is


"(x+2)^2+(y-4)^2+(z+6)^2=36"

(b)

Since the sphere touches the xz-plane, its radius is the distance from its center, "(-2, 4, -6)," to the xz-plane, which is "4." Therefore "r = 4" and an equation of the sphere is


"(x+2)^2+(y-4)^2+(z+6)^2=16"

(c)

Since the sphere touches the yz-plane, its radius is the distance from its center, "(-2, 4, -6)," to the yz-plane, which is "2." Therefore "r = 2" and an equation of the sphere is


"(x+2)^2+(y-4)^2+(z+6)^2=4"


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