Find all of the points of the form (x,-1) which are 7 units from the point (-2,5)

Use distance formula

 

sqrt (x1-x2)^2 + (y1-y2)^2  =  7

sqrt ((x- -2)^2 + (-1-5)^2 ) = 7        square both sides and expand

 

  x^2 +4x +4   + 36  = 49

x^2 +4x -9 = 0                                use quadratic formula   x = -2 +- sqrt 13          points  : (-2+sqrt13 , -1)  and  (-2-sqrt13 , -1)