Question

Find all points (x,y) that are 13 units away from the point (2,7) and that lie on the line x-2y=10.

Answer 1

symbolize and solve equations using:
average prices of three items A, B, C is $ 16000, if the price of the item a is twice the sum of the prices of the items B and

Answer 2

symbolize and solve equations using:
average prices of three items A, B, C is $ 16000, if the price of the item a is twice the sum of the prices of the items B and C

Answer 3

√((x-2)^2 + (y-7)^2 = 13
square both sides and expand
x^2 - 4x + 4 + y^2 - 14y + 49 = 169
x^2 - 4x + y^2 - 14y = 116
but x = 10+2y
sub that into the first equation

(10+2y)^2 - 4(10+2y) + y^2 - 14y = 116
100 + 40y + 4y^2 - 40 -8y + y^2 - 14y = 116
5y^2 + 18y - 56 =0
(y-2)(5y + 28) = 0
y = 2 or y = -28/5

if y = 2, then x = 10+2(2) = 14 ---> point is (14,2)
if y = -28/5, x = 10 + 2(-28/5) = -6/5 ---> point is (-6/5 , -28/5)