A is the point (0,-4) and B is the point (0,10). AB is the diameter of a circle which passes through the point C (p,0) where p is positive. Find the exact value of p. Give your answer in its simplest form? PLEASE HELP

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1 Answer
Nov 6, 2017

2sqrt10.210.

Explanation:

Given that the points (pts.) A, and, BA,and,B are the extremities of a

diameter, the mid-pt. PP of the segment ABAB is the centre of the

circle.

We have, P=P((0+0)/2,(10-4)/2)=P(0,3).P=P(0+02,1042)=P(0,3).

Now, the pts. A(0,-4), and, C(p,0); p>0A(0,4),and,C(p,0);p>0 both lie on the

circle, therefore, the radius rr is given by the distances (dists.)

AP, CP.AP,CP.

Using the dit. formula, we then, have,

AP^2=r^2=CP^2.AP2=r2=CP2.

:. (0-0)^2+(3+4)^2=r^2=(p-0)^2+(0-3)^2.

:. 49=p^2+9 rArr p^2=40.

:. p=+-sqrt40=+-2sqrt10.

But, as p>0, p=+2sqrt10.