✔ 最佳答案
(a)
Since the circle touches the x-axis and the y-axis,
we may assume that the eq. is ( x - r )^2 + ( y - r )^2 = r^2
Substitute P(8,4) into the eq. , we obtain
( 8 - r )^2 + ( 4 - r )^2 = r^2
r^2 - 24r + 80 = 0
( r - 4 )( r - 20 ) = 0
r = 4 , 20
So
A = ( 4 , 0 ) or ( 20 , 0 ) ... Ans
B = ( 0 , 4 ) or ( 0 , 20 ) ... Ans
(b)
Hence, two possible eq. are :
( x - 4 )^2 + ( y - 4 )^2 = 4^2 or ( x - 20 )^2 + ( y - 20 )^2 = 20^2 ... Ans
(c)
When r = 4
the slope of AP = m(AP) = ( 4 - 0 ) / ( 8 - 4 ) = 1
m(AB) = ( 4 - 0 ) / ( 0 - 4 ) = - 1
m(AP) * m(AB) = - 1 , so AP ⊥ AB
When r = 20
m(AP) = ( 4 - 0 ) / ( 8 - 20 ) = - 1/4
m(AB) = ( 20 - 0 ) / ( 0 - 20 ) = - 1
m(AP) * m(AB) = 1/4 ≠ - 1 , so AP is not perpendicular to AB
Ans for (c) : The eq. is ( x - 4 )^2 + ( y - 4 )^2 = 4^2 , and the diameter is 8 .