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Locus and the parabola (1 Viewer)

Roserox

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1 a) find the equation of the locus of point P, which is equidistant from fixed points A(3,5) and B(-1,2).

I've already figured this out. Equation of the locus of point P is 8x + 6y -29.

b) show that is locus is the perpendicular bisector of line AB.
Could someone please help me with part b) of this question. In detail please! Hopefully I've done part a) right.
 

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