圖中圓的圓心是(2,4),圓面積是25乘3.14.若有若(6,K)在該圓上,求K的所有可能值

Take π = 3.14

Let r be the radius of the circle

πr2 = 25 X 3.14

3.14r2 = 25 X 3.14

r2 = 25

r = 5 or -5 (rejected)

So, radius of the circle is 5

Equation of the circle:

(x - 2)2 + (y - 4)2 = 52

x2 + y2 – 4x – 8y – 5 = 0

As the circle passes through (6 , k)

Put (6 , k) into the equation, we get

(6)2 + k2 – 4(6) – 8k – 5 = 0

k2 – 8k + 7 = 0

(k - 7)(k - 1) = 0

k = 1 or 7

So, the value of k is 1 or 7.

Take π = 3.14



Let r be the radius of the circle



πr2 = 25 X 3.14



3.14r2 = 25 X 3.14



r2 = 25



r = 5 or -5 (rejected)



So, radius of the circle is 5



Equation of the circle:



(x - 2)2 + (y - 4)2 = 52



x2 + y2 – 4x – 8y – 5 = 0



As the circle passes through (6 , k)



Put (6 , k) into the equation, we get



(6)2 + k2 – 4(6) – 8k – 5 = 0



k2 – 8k + 7 = 0



(k - 7)(k - 1) = 0



k = 1 or 7



So, the value of k is 1 or 7.

跟上面的仁兄一样~