Question is:

The variable chord on the parabola with equation subtends a right angle at the origin . By taking as and as , find a relation between and and hence show that passes through a fixed point on the .

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- Mar 14th 2008, 10:57 PMrednestCoordinate systems help!
Question is:

The variable chord on the parabola with equation subtends a right angle at the origin . By taking as and as , find a relation between and and hence show that passes through a fixed point on the . - Mar 15th 2008, 02:12 AMMoo
Hello,

If you've learnt vectors, you can say that :

is

is

Then, you'll have a relation between and

To find the fixed point, on the x-axis, find the equation of (PQ) (form y=ax+b) and solve it for the point of 0-ordinate (on the x-axis, all points have 0-ordinate) - Mar 15th 2008, 02:27 AMearboth
The staionary vector pointing at P is and the staionary vector pointing at Q is

Since these 2 vectors subtend a right angle the dot product of the vectors must be zero:

That means:

The first case happens if P = O or Q = O.

From the 2nd case we get: . Therefore the coordinates of the point Q become:

I only write t if is meant.

Calculate the equation of the line PQ:

Solve for y.

Now choose 2 different values for t, for instance t = r or t = s. You'll get 2 different equations for 2 different lines. Calculate the coordinates of the point of intersection between these 2 lines.

You'll get the Point I(4, 0)

I've attached a sketch of the situation.