Locating a Moving Point P: x+y=9

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The problem involves finding the locus of a moving point P, where the length of the tangent from P to the circle defined by x²+y²=16 equals the distance from P to the point (8,8). To solve this, the length of the tangent can be expressed mathematically, and the distance from P to (8,8) can also be calculated. By equating these two expressions, the locus of P can be determined. The solution leads to the conclusion that the locus is represented by the straight line equation x+y=9. This demonstrates the relationship between the tangent length and the distance from a fixed point.
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Homework Statement



A moving point P is such that the length of the tangent from P to the circle x2+y2=16 is equal to the distance of P from point (8,8). Show that the locus of P is the straight line x+y=9.

Homework Equations





The Attempt at a Solution



I sketched a graph for this, but it doesn't seems to help me a lot in solving this question. Can anyone give me some hints? Thanks...
 
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Well, let the point P be (a,b). What is the length of the tangent to the circle? What is its distance from (8,8)? Equate the two.
 

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