The abscissa of a point is 2/5 of its ordinate, find the point if it is 5 units from (-2,2)?

Question

The abscissa of a point is 2/5 of its ordinate, find the point if it is 5 units from (-2,2)

Answer 1

(x + 2)^2 + (2x/5 - 2)^2 = 25
x^2 + 4x + 4 + 4x^2/25 - 8x/5 + 4 = 25
25x^2 + 100x + 100 + 4x^2 - 40x + 100 = 625
29x^2 + 60x - 425 = 0
x = ( - 60 ± √(3600 + 4*29*425))/58
x = ( - 60 ± √(3,600 + 49,300))/58
x = ( - 60 ± √52,900)/58
x = ( - 60 - 230)/58,( - 60 + 230)/58
x = - 290/58, 170/58
x = - 5, 2.9310
y = - 2, 1.1724
P(x,y) = (- 5, - 2), (2.9310, 1.1724)