Finding the locus, seriously need help quick

1. Apr 2, 2009

help4drdu

1. Given the points A(1,4) and B(-3,2), find the equation of each locus of the pont P(x,y), a) angle APB is a right angle
b) P is equidistant from A and the x-axu

2. Apr 2, 2009

Mentallic

ok for:

a) The key point is that it's a right angle, so simply use $$M_{PA}M_{PB}=-1$$ where M is the gradient of each line. You will end up with an equation in x and y, which is your locus.

b) Since P is equidistant from the x-axis (y=0) and A(1,4) use the distance formula.

3. Apr 2, 2009

help4drdu

thanks for your quick response, but could you please explain a) i seem to be having trouble i understanding the equation you have written.

4. Apr 2, 2009

Mentallic

Sure, no problem.

Are you familiar with the fact that if two lines are perpendicular to each other, their gradients multiply to give -1?

Such as y=x and y=-x, their gradients multiplied together give: (1)(-1)=-1 and thus these lines are perpendicular (right angles) to each other.

So $$M_{PA}$$ is the gradient of the line PA, which is found by using the gradient formula,
$$\frac{y_2-y_1}{x_2-x_1}$$

If you're still unsure, just ask

5. Apr 2, 2009

help4drdu

Thanks! That makes it a lot more clearer now. Also thanks for your fast responses. =] Hope you have a great day =]

6. Apr 2, 2009

Mentallic

Glad I could help Have a great day too.