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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Answer 1 · 2017-11-06T18:20:27

# 2sqrt10.#

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

diameter, the mid-pt. #P# of the segment #AB# is the centre of the

circle.

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

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

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

#AP, CP.#

Using the dit. formula, we then, have,

#AP^2=r^2=CP^2.#

#:. (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.#