# Thread: Coordinate geometry and perpendicular distance

1. ## Coordinate geometry and perpendicular distance

1) Find the equations of the lines which pass through the point (1,2) and have perpendicular distance 1 from the origin.

The equation of a line passing through (1,2) is y = (2-p) + px for any constant p. I got $\displaystyle |\frac{p-2}{\sqrt(1+p^2)}|=1$ and therefore $\displaystyle p=\frac{3}{4}$ and the equation of the line is $\displaystyle y=\frac{5}{4} + \frac{3}{4}x$. I just need to check: is this the only possible equation that satisfies the above conditions?

2. Originally Posted by anthill
1) Find the equations of the lines which pass through the point (1,2) and have perpendicular distance 1 from the origin.

The equation of a line passing through (1,2) is y = (2-p) + px for any constant p. I got $\displaystyle |\frac{p-2}{\sqrt(1+p^2)}|=1$ and therefore $\displaystyle p=\frac{3}{4}$ and the equation of the line is $\displaystyle y=\frac{5}{4} + \frac{3}{4}x$. I just need to check: is this the only possible equation that satisfies the above conditions?
Your question asks you to find the tangents to a circle with the origin as it's center and the radius r = 1 from the point P(1, 2).

Therefore the line x = 1 satisfies the given conditions but can't be expressed by an equation using y = mx +b.

3. Thanks, can't believe I overlooked that...