Locus questions (1 Viewer)

[Joshmosh2]

Greetings, I have a couple maths questions to ask..
Circle and locus-
1. A(4,2) and B(-2,-8). Find the locus of a point P(x,y) that moves so the angle APB is a right angle.
2. A point P(x,y) moves so that its distance from (3,4) is proportional to its distance from (-1,-2). Find the equation of the locus P if the origin is a point on the locus.
3. A is a point where the circle with equation x^2+y^2 =16 cuts the X-axis. Find the locus of the midpoints of all chords of this circle that contain the point A

There is also a parabola question that I am unsure about
P(-1,1/4) and Q(2,1) lie on a parabola x^2=4y. Show that PQ is not a focal chord.
So basically, i got the equation of the focal chord x-4y+2=0, and worked from there.
What I thought was for PQ to be a focal chord, there has to be two distinct points.
So basically, I used the quadratic equation, and after some working out, got x=+-2 and x=+-1.
I'm not sure if this logic is correct, I just need some confirmation.

Thanks,

 

[Drongoski]

Q1

You use the condition: (gradient of PA) x (gradient of PB) = -1

gradient of PA = (y-2)/(x-4) etc

 

[Joshmosh2]

Thanks, but how would I do question 2?