Conics (1 Viewer)

[GaganDeep]

Hey, i got this question, COuld you also please post a diagram aswell. THanks inadvandce

7) P(acos(theta),bsin (theta) and Q (acos (thai),b sin (thai) lie on the ellipse (normal one)
if PQ subtends a right angle at (0,0) show that tan (theta)tan(thai)= -b^2/a^2
b) ud PQ subtends a right angle at (a,0) show that tan(theta/2)tan(thai/2)= -b^2/a^2
Thanks

 

[haboozin]

Hey, i got this question, COuld you also please post a diagram aswell. THanks inadvandce

7) P(acos(theta),bsin (theta) and Q (acos (thai),b sin (thai) lie on the ellipse (normal one)
if PQ subtends a right angle at (0,0) show that tan (theta)tan(thai)= -b^2/a^2
b) ud PQ subtends a right angle at (a,0) show that tan(theta/2)tan(thai/2)= -b^2/a^2
Thanks

the first part is very easy

what do you think about when it says right angle

m1.m2 = -1

so basicly b^2/a^2cot@cot& = -1
so -b^2/a^2 = tan@tan&

b. this ones a bit more difficault, since its not exactly 0,0
but if u get the gradient for P and Q and do the same thing as above you get the answer..




i used to never believe in diagrams, but it helped me with conics, so maybe you sohuld draw diagrams

 

[c0okies]

haboozin.. for question 1.. isnt that formula for the gradient the gradient of a tangent?

 

[Riviet]

Remember that if m₁m₂=-1, then it means that the two gradients, m₁ and m₂ are perpendicular, hence the right angle.