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Math Help - Coordinate geometry and perpendicular distance

  1. #1
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    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 |\frac{p-2}{\sqrt(1+p^2)}|=1 and therefore p=\frac{3}{4} and the equation of the line is y=\frac{5}{4} + \frac{3}{4}x. I just need to check: is this the only possible equation that satisfies the above conditions?
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  2. #2
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    Quote Originally Posted by anthill View Post
    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 |\frac{p-2}{\sqrt(1+p^2)}|=1 and therefore p=\frac{3}{4} and the equation of the line is 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.
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  3. #3
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    Thanks, can't believe I overlooked that...
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