You are to find an equation for a plane and an equation for a sphere. Recall tha

Question

You are to find an equation for a plane and an equation for a sphere. Recall that these equations are not unique. To get the equations given in the answers below, you should use the procedures illustrated in class (attendance is mandatory). Choose the answer that best fills in the blank from the possibilities below. Then circle the appropriate letter after the question. 7. (4 pts.) Let P be the plane through the origin and parallel to the plane with equation 4x +2 y = 3 z +10. An equation for P is BD. BE. CD. CE. DE. ABC 8. (4 pts.) Let S be the sphere of radius 3 with center at (2,3,0). An equation for S is A. B. C. D. E. AB. AC. AD. AE. BC. BD. BE. CD. CE. DE. ABC. Possible answers for this page A. 4x + 2 y +329-10 B. 4x +2 y-3z+10, C. 4x +2 y _ 3 z = 0, D. 2x + 3 y=10 E. 4x +2 y= 10 AB. 4x +2 y-3z =10, AC, 4x + 2 y + 3z =0, AD. 2x +3 y=3 AE. (x+2)2 + (y + 3)-9, BC. (x-2)2 + (y + 3,-+2=9, BD. (x+2)2 + (y-3,-+2=9, BE. (x-2)2 + (y-3)2 = 3, CD(x-2)2 + (y3,-+2 = 9, CE. (x +2)2 + (y-3)2 +2 = 3, DE. (x +2)2 + (y + 3)2 = 3, ABC. None of the above. Possible points this page = 8, POINTS EARNED THIS PAGE-

Explanation / Answer

7)

given plane 4x+2y =3z+10

=> 4x+2y -3z=10

general equation of plane parallel to 4x+2y -3z=10 is 4x+2y -3z=d

required plane passes through origin (0,0,0)

=>4*0+2*0 -3*0=d

=>0+0-0=d

=>d=0

so equation of plane  parallel to 4x+2y =3z+10 and passing through origin is 4x+2y-3z=0

option C

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8) equation of sphere with radius r and center (h,k,l) is (x-h)2+(y-k)2 +(z-l)2=r2

given radius r =3, center (h,k,l)=(2,3,0)

=> (x-2)2+(y-3)2 +(z-0)2=32

=> (x-2)2+(y-3)2 +z2=9

option CD

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