Question

Prove or disprove that the given point lies on the given circle. Point (4,-4) with center (1,0) and containing the point (1,5)

THANK YOU :)

Answer 1

circle with center (1,0) and containing the point (1,5)
I would use the equation of a circle:
\[ (x-h)^2 + (y-k)^2 = r^2 \]
where the center is (h,k) and the radius is r
we know the center is (1,0) so we can write
\[ (x-1)^2 + y^2 = r^2 \]
(notice we can write (y-0)^2 as just y^2 )
to find the radius, use the distance formula to find the distance from the center (1,0) to the point (1,5)
we will find the distance is 5, so r=5, and the full equation is
\[ (x-1)^2 + y^2 = 25 \]
(remember that r^2 means r*r , and r is 5, so 5*5 or 25)
now test the point (4, -4) in that equation:
\[ (4-1)^2 + (-4)^2 =? 25 \]
will we get 25 ? if we do, then (4, -4) is on the circle.