CAn some 1 SOlve this locus Q????2 (1 Viewer)

[david2004]

A) Given the points A(4,0), B(-2,0) and P(X,Y) find the gradient of ap and bp. I did that and my answer was

Y/x-4 and y/x+2 respectively

then part b states

(B) Hence show that the equation of the locus of the point P(x,y)
which moves so that angle APB is a right angle is x sqaured +y squared - 2x - 8=0

thats how the qustion is worded exactly. I would appreciate some help Thx.

also posted this in maths forom but i figured it had an increased chance of being answered faster if i posted it here 2.

 

[BlackJack]

Okay, here's how you do it...
you have found the two gradients in part a, which is connected to a property of the right angle in part b.

part b stats that th point P has to form a right angle APB.
So, PA is perpendicular to PB, from this result.
We know that for this to happen, the two gradients multiply to give -1.
i.e. m_PA*m_PB = -1
Therefore,
( Y/(x-4) ) * ( Y/(x+2) ) = -1

And you can algebraically deduct the answer from there on.

 

[victorling]

yep