If we know that plane α ‖ plane β, line L ⊂ plane α, point P ∈ line L, and the distance between planes α and β is 8, then the distance to point P in β is 10, and the trajectory of the point with the distance to l of 9 is () A. A circle B. four points C. two straight lines D. two points

If we know that plane α ‖ plane β, line L ⊂ plane α, point P ∈ line L, and the distance between planes α and β is 8, then the distance to point P in β is 10, and the trajectory of the point with the distance to l of 9 is () A. A circle B. four points C. two straight lines D. two points

As shown in the figure: for pH ⊥ β, h is perpendicular, then pH = 8. For a straight line m ∥ L through h, then M is the projection of L in plane β. For HA ⊥ m, and ha = 17, pH = 8, then PA ⊥ m, ≁ PA ⊥ L can be obtained from the three perpendicular theorem, so PA = 9. For am ∥ m, and am = 19, there is Pythagorean theorem, then MP = 10, so m is on the desired trajectory. And point m is in plane β, so there are four M satisfying the condition, so B is selected