Squaring in a locus (1 Viewer)

[highshill]

Why do we square in the beginning of a locus problem and then use a distance formula? Can someone solve this question explaining what is happening in each step:

Find the equation of the circle with centre Q(3,4) and radius r

 

[1729]

Why do we square in the beginning of a locus problem and then use a distance formula? Can someone solve this question explaining what is happening in each step:

Find the equation of the circle with centre Q(3,4) and radius r

In the distance formula the whole expression is under a square root. So in locus problems where two distances are equal or proportional then we often square both sides at the beginning to immediately eliminate the square root.

 

[highshill]

So why do we use distance formula and not another formula?

 

[1729]

So why do we use distance formula and not another formula?

It depends on the question. For example if they say a point P(x,y) moves so that it is equidistant from the line y = -a and the point S(0, a) then we can say that PM = PS to find the locus of P, where PM is the perpendicular distance from P to the line. From here we can say that (PM)^2 = (PS)^2 to eliminate the square root that comes from the distance formula (since both PM and PS are distances). What other formulae are you referring to?

 

[highshill]

Okay, so when we square Both sides do we square the distance formula too