Locus question (1 Viewer)

[Wonder]

From Maths in Focus Prelim Test Yourself 11

Find the equation of the locus of a point that is always 3 units from the line 4x -3y -1 = 0

Thanks!

 

[Timske]

Apply the Perpendicular distance formula and you should have two cartesian equations

 

[Wonder]

OH. Thank you!

 

[hamster-lol]

Look for hints when doing these sorts of questions.

Like the line is linear, and you want to find the locus such that a point is always a certain distance from that line.

You should be able to notice that the perpendicular distance formula is needed:

 

[RealiseNothing]

Disgusting, ewwwwwwwwwwwwww.

 

[hamster-lol]

Disgusting, ewwwwwwwwwwwwww.

It's right.....

 

[braintic]

Another method - no easier but avoids perpendicular distance:

Pick a point that lies on the given line, say (1,1).
Write down the equation of a circle whose centre is at this point, with radius 3.
The new lines must have the form 4x-3y+c=0. Solve this simultaneously with the equation of the circle, and use the discriminant (equal roots for tangent) to find c.