Quick Question (1 Viewer)

[5647382910]

This may sound stupid but im puzzled with this:
at = at^3 + 2at (this is to do with parametrics+ parabola btw), are we allowed to divide both sides by at??? if not, why not?
i tried dividing both sides by a and then minusing both sides by t and this gave me the correct answer, But how come wen i divide by t i get the wrong answer?????

 

[Trebla]

This may sound stupid but im puzzled with this:
at = at^3 + 2at (this is to do with parametrics+ parabola btw), are we allowed to divide both sides by at??? if not, why not?
i tried dividing both sides by a and then minusing both sides by t and this gave me the correct answer, But how come wen i divide by t i get the wrong answer?????

You are only allowed to divide both sides by some factor ONLY IF THAT FACTOR IS NON-ZERO. When you divide by t, you've assumed that t is non-zero (if t = 0, dividing both sides would be non-sense). However, in this equation, t = 0 is in fact a solution. If you divide by t its a bit like saying 2 x 0 = 3 x 0 (which is true), divide by zero gives 2 = 3 which is clearly false.
The reason when you divide by a and it gives the answer, is because a is not zero.
at = at³ + 2at
at³ + at = 0
at(t² + 1) = 0
=> t = 0 (as t² = - 1 gives no real solution)

 

[5647382910]

You are only allowed to divide both sides by some factor ONLY IF THAT FACTOR IS NON-ZERO. When you divide by t, you've assumed that t is non-zero (if t = 0, dividing both sides would be non-sense). However, in this equation, t = 0 is in fact a solution. If you divide by t its a bit like saying 2 x 0 = 3 x 0 (which is true), divide by zero gives 2 = 3 which is clearly false.
The reason when you divide by a and it gives the answer, is because a is not zero.
at = at³ + 2at
at³ + at = 0
at(t² + 1) = 0
=> t = 0 (as t² = - 1 gives no real solution)

ok i see, thanks for your help

 

[5647382910]

Im stuck again,
in this question u have to find the intersection (point R) of the normals at points P(2ap,ap^2) and Q(2aq,aq^2)
for finding the y coordinate ive got:
py = 2ap + ap^3 + apq(p+q).... and if i divide by p i get the solution.... P can be zero, cant it? therefore, why can we divide by it???

 

[Trebla]

When you found the gradient of the normal, you've assumed p is non-zero in the process.
The gradient of the tangent at P is p, so the gradient of the normal at P is -1/p.
Since you've used -1/p in the equations, you've automatically assumed p cannot be zero, otherwise the gradient of the normal is undefined.