Question

Find equations for all the planes that intersect the y-axis at y = 1 and the z-axis at z = 2, and are tan- gent to the sphere (x - 2)2 + y2 + z2 = 4. Do not use calculus.

Answer 1

The equations for the planes that intersect the y-axis at y = 1 and the z-axis at z = 2, and are tangent to the sphere (x - 2)² + y² + z² = 4 are x = 0 and x = 4.

Step-by-step explanation:

To find the equations for the planes, we can start by finding the equations for the lines that intersect the y-axis at y = 1 and the z-axis at z = 2. These lines can be represented by the equations x = 0 and x = 2, respectively. Since the planes are tangent to the sphere (x - 2)² + y² + z² = 4, the distance from the center of the sphere to the planes is equal to the radius of the sphere.

The center of the sphere is (2, 0, 0), so the distance from the center to the planes is 2. Therefore, the equations for the planes are x = 0 and x = 4.