The line - higher math problem

Areq

the lenght of the perpendicular to a line from the origin is 5 units . the line passes through the point (3,5) . Find the equations of two such lines.


how to ?

ShonyBoulders

Well if it's a line from the origin...

Maybe_Memories

Areq wrote: »

the lenght of the perpendicular to a line from the origin is 5 units . the line passes through the point (3,5) . Find the equations of two such lines.


how to ?

Throw the info into your distance formula, get the slope of the line and the equation of the line, then use all that to get the perpendicular lines. you'll probably get x^2 and y^2 so that'll give you the two possibilities

MathsManiac

Use the general form of the line: y = mx +c, and try to use the given conditions to find m and c, as follows:

Sub. in the point (3, 5), and use that to write c in terms of m, so now you have the equation of the line in terms of m alone (and x and y, obviously).

Then, use the formula for the distance from a point to a line to write a second equation. This should be in terms of m alone, and be of the form of a modulus divided a square root equal to a constant.

Multiple across by the denominator, and square both sides and you'll have a quadratic in m. Should be ok from there.