Analytic Geometry

Which of the following is the standard form of the sphere?

• - 3x - 4z - 52 = 0

• ( x ²+4) + ( y ²- 3) + ( z ² - 7 ) = 56

• ( x + 4 ) ² + ( y - 3) ² + ( z - 7 ) ² = 74

• 3x² + 3y² + 3z² + 6 x- 24y+ 36 z + 217 = 0

Find the equation of the sphere

• ( x - 4 ) ² + ( y - 3) ² + ( z - 12 ) ² = 169

• ( x - 2 )² + ( y -3 )² + ( z - 4 )² = 16

• ( x - 1 ) ² + ( y - 2) ² + ( z - 3 ) ² = 9

• ( x + 1 ) ² + ( y - 4) ² + ( z + 6 ) ² = 16

Find the volume of the sphere with R = 7

• 1372/3π

• 1436.75504

• 196π

• 615.7521

Find the center of this sphere: x² + y² + z² + 4x - 6z = 0

• C (2, 0, -3)

• C (-2, 0, 3)

• C (-2, 0, -3)

• C (2, 0, 3)

Find the radius of this sphere: x² + y² + z² - 2x + 4y = 0

(V-root of)

• V5

• V6

• 5

• 2V6

Is tangent plane perpendicular to the sphere?

• TRUE

• FALSE

A plane is tangent to a sphere at the point P if it intersects the sphere in any point(-s)

• True

• False

Write the equation of this sphere: C (1, 2, 3) tangent to the xy-plane.

• ( x - 1 ) ² + ( y - 2) ² + ( z - 3 ) ² = 4

• ( x - 1 ) ² + ( y - 3) ² + ( z - 2 ) ² = 1

• ( x - 1 ) ² + ( y - 2) ² + ( z - 3 ) ² = 9

• ( x - 1 ) ² + ( y - 2) ² + ( z - 3 ) ² = 16

Find the equation of the tangent to the sphere ( x - 0 )² + ( y - 2 )² + ( z - 2 )² = 6 at point (-2, 1, 3)

• 2x + y - 2z + 8 = 0

• x - 2y + z = -6

• 2x + y - z + 9 = 0

• 2x + y - z + 6 = 0

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