# Coordinate geometry and perpendicular distance

• Oct 26th 2010, 03:03 AM
anthill
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?
• Oct 26th 2010, 03:44 AM
earboth
Quote:

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.
• Oct 26th 2010, 04:03 AM
anthill
Thanks, can't believe I overlooked that...