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Hi :) how to do question 7 ?

Hi :) how to do question 7 ?-example-1
User Mac Adada
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Answer:

Explanation:

We khow that the equation of a circle is written this way :

(x-a)²+(y-b)²=r² where (x,y) are the coordinates of the cercle's points and (a,b) the coordinates of the cercle's center and r the radius .

Our task is to khow the values of a and b :

  • We khow that the center is lying on the line 3x+2y=16⇒ 2y=-3x+16⇒ y=
    (-3)/(2)x+8
  • We khow that the points P and Q are two points in the cercle
  • Let Ω be the center of this cercle
  • we can notice that : PΩ AND QΩ are both equal to the radius ⇒ PΩ=QΩ= r
  • So let's write the expression of this distance using vectors KHOWING THAT Ω(a,b)
  • Vector PΩ(a-4,b-6) and Vector QΩ(a-8,b-2)
  • PΩ=
    \sqrt{(a-4)^(2)+(b-6)^(2) } and QΩ=
    \sqrt{(a-8)^(2)+(b-2)^(2) }
  • Let's substitute a by x and b by y
  • PΩ=QΩ we substitute each distance by its expression
  • After simplyfying the expressions we get finally : -12+8x-8y=0
  • now we have -12x +8x-8y=0 and the line equation 3x+2y-16=0
  • these are simultanious equations so after solving them we get x=3.8 wich is approximatively 4 and y=2
  • we substitute a by 4 and y by 2 in PΩ to get the radius
  • we get r =
    \sqrt{(4-4)^(2)+(2-6)^(2) } = 4
  • so r²= 16
  • then the equation is : (x-4)²+(y-2)²=16
User ArielB
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