write an equation which must be true if the line from p(x,y) to a(25,0) is perpendicular to the line from P(x,y) to the center of the circle x^2+y^2=400

Question

write an equation which must be true if the line from p(x,y) to a(25,0) is perpendicular to the line from P(x,y) to the center of the circle x^2+y^2=400

Answer 1

I will make the assumption that P is on the circle

then if the centre is the origin , called O
then slope PO = -1/slope PA

y/x = -1/(y/(x-25) )
y/x = (25-x)/y

y^2 = 25x - x^2
but y^2 = 400 - x^2

400-x^2 = 25x - x^2
25x = 400
x = 16