What is the equation of the circle that has its center at (0,0) and is tangent to the line with equation 3x-4y = 10?

Question

campbell_st · Answer

and the equation of the circle is 

$$x^2 + y^2 = r^2$$

the goal is to find r, the radius of the circle... 

so they there is an equation that lets you find the perpendicular distance from a line to a point. 

the tangent is always perpendicular to a radius... so if you find the distance from 

3x - 4y = 10  to the point (0, 0) you'll be able to find r.... 

the formula is $$d = \frac{\left| Ax + By + C \right|}{\sqrt{A^2 + B^2}}$$

so you have x = 0, y = 0, A = 3, B = -4 and C = -10

hope it helps