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# a bakery makes ginger bread men each 14cm high with a circular head and body

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a bakery makes ginger bread men each 14cm high with a circular head and body

the equation of the body is x^2 + y^2 -10x -12y +45 = 0

and the line of centres is parallel to the y axis

find the equation of the head

Oct 28, 2018

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what a bizarre question...

Well let's get the equation of the body in standard form so we can see what we're dealing with.

$$x^2+y^2 - 10x - 12y + 45 = 0\\ \text{complete the two squares on the left hand side}\\ (x-5)^2 - 25 + (y-6)^2 - 36 + 45 = 0 \\ \\ (x-5)^2 + (y-6)^2 = 16 \\ \\ \text{so the body is a circle centered at }(5,6) \text{ with a radius of 4 cm}\\ \\ \text{The overall height is 14cm, 8cm of this is the body, so the diameter of the head is 6cm}\\ \text{And the head must be centered at }(5, 11), \text{ i.e. one radius above the top of the body}\\ \\ \text{so the equation of the head centered at }(5,11) \text{ with radius 3 is}\\ (x-5)^2 + (y-11)^2 = 9$$

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Oct 28, 2018