Answer: The equation of the sphere with the center and radius
b) The intersection of this sphere with the y z-plane the x- co-ordinate
is zero(i.e., x = 0 )
Step-by-step explanation:
a) The equation of the sphere having center (h,k,l) and radius r is
Given center of the sphere (3, -9, 3) and radius 5
on simplification , we get solution
Final answer :-
b) The intersection of this sphere with the y z-plane the x- co-ordinate
is zero(i.e., x = 0 )
For a better understanding of the solution given here please find the attached file which has the relevant diagram.
To answer this question we will have to make use of <u>the Isosceles Triangle Theorem</u> which states that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle. Thus, as a corollary we know that is EF is the angle bisector of the vertex angle ∠E, then, EF is the perpendicular bisector of the of the base DK.
Please follow the diagram of a complete understanding of the logic and the solution.
As EF is the angle bisector as given in the question, thus we will have:
.
Also, from the Theorem we know that KF will be half of DK and thus, KF will be: centimeters.
Likewise, from the same theorem we have:
the distance form X to Y is clearly -6 to 0 is 6 units, and 0 to 8 is 8 units, so 6 + 8 = 14 units.
now, for XZ and ZY we can simply use as stated, the distance formula to get those and then add them all to get the perimeter.