Find the point on the sphere left parenthesis x minus 4 right parenthesis squared(x−4)2 plus+y squared 2 plus+left parenthesis z plus 6 right parenthesis squared(z+6)2 equals=44 nearest to a. the xy-plane. b. the point left parenthesis 7 comma 0 comma negative 6 right parenthesis(7,0,−6).

a) It is the set of point in the the circumference with equation .

b) (10.6, 0, -6 )

Step-by-step explanation:

a) The centre of the sphere is (4,0,-6) and the radio of the sphere is . Since |-6|=6 < 6.6,  then the sphere intersect the xy-plane and the intersection is a circumference.

Let's find the equation of the circumference.

The equation of the xy-plane is z=0. Replacing this in the equation of the sphere we have:

, then .

b) Observe that the point (7,0,-6) has the same y and z coordinates as the centre and the x coordinate of the point is greater than that of the x coordinate of  the centre. Then the point of the sphere nearest to the given point will be at a distance of one radius from the centre, in the positive x direction.

(4+, 0, -6)= (10.6, 0, -6 )

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.