唔識做功課77......?

2016-01-27 1:40 pm

Circle C passes through P(8,4). It touches the x-axis and the y-axis at point A and B respectively.
a) Find two sets of the coordinates of A and B.
b) Find two possible equations of the circle C.
c) Which equation in (b) represents a circle such that AP perpendicular AB? Hence,find the diameter of that circle.

回答 (2)

Lopez

2016-01-28 7:47 am

✔ 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 .

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用戶40441

2016-01-28 1:43 pm

????睇你做就好簡單，自己做就毫無頭緒。。。師兄，唔該晒!

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