over9000 questions thread

[TrueTears]

Let














(thanks to /0 for this method)
I will also post the way i did it, but much harder so follow this one

[TrueTears]

let Q = (a,b)



squaring both sides leaves ...[1]

But we know line PS and QS must have the same gradient (since they are collinear)

so ...[2]

Solve these 2 equations in the graphics calc which leaves you

and

notice when you solve on the calc put like and y = or else the equation comes out to be some random crap lol. then just sub in the for x and for y after you get an answer

but yeah follow the other method, much easier

[Over9000]

As varies, the point P moves around the ellipse. As P moves, so does Q. Find the cartesian equation of the locus of Q as varies. State the type of curve traced out by Q and give the coordinates of the centre of this curve. This is a continuation of the question before it.

[TrueTears]

we know and

rearranging leaves us with and

square both sides leaves us with and

add those two and we get



This is an ellipse centered at

[Over9000]

Thanks for all your help truetears

[Over9000]

2. A radar tracking facility tracks a plane flying in a straight line. With the radar facility as the origin, the plane's initial and final position vectors are a = 2i + 8j + k and b = 8i -4j + 13k respectively.
a) Find a unit vector , u , in the direction of the motion of the plane.

this i found to be

b) The position vector of the plane, p, when it is closest to the radar can be expressed as is a real number. find the value of \gamma and hence the plane's position when it is closest to the radar facility.

[TrueTears]

Thanks for kamil for showing me the the method but this is my working out:








using the calc to solve

[Over9000]

thanks

[Over9000]

Lines y = 2x and y = 10-2x are the asymptotes of a hyperbola of the form.
Find the values of p and q

[TrueTears]

p and q are the midpoint of the hyperbola and the mid point of a hyperbola always happen to the at the intersection of the asymptotes. so just simplify solve the simultaneous equation y = 2x and
y = 10-2x to find p and q

[Over9000]

thanks man, I get it now, easy 8-)

[Over9000]

show that can be represented by the parametric equations
and

[TrueTears]

so
and

rearrange x to and y to

square both sides and minus

so which using trig identities remember so

then just simplify, im sure you can do it from here

[Over9000]

Then determine a range of values of t which will represent the hyperbola without duplication?

[Over9000]

Points A,B and C are and respectively.
How do you do part h, where unit vector OA is
Hence show that vector OP = j+k, where P is the point on vector OA nearest to B