Find the coordinates of any point on the line with equation y=3x and 5 units from (2,1) ?

Question

hint: let (a,3a) lie on the line y=3x

Answer 1

Ok. we'll do it your way.

Let the point A(a,3a) lie on the line y=3x. This point is supposed to be 5 units from (2,1) (Let's call this point B), So it should be on a circle with a radius of 5 units and with its center on point B, right? what's the equation for such a circle?

(x-2)^2+(y-1)^2=25

Now put the coordinates of point A in the equation. You'll have:

(a-2)^2+(3a-1)^2=25

Solving for a, you'll get:

a= -1 , 2

So the circle intersects with line y=3x in two points: A1(-1,-3) and A2(2,6)