Parametrics (1 Viewer)

[unity-]

On the parabola x²=4ay, the normal from a point P (parameter p) meets the parabola again at R (parameter r). By using the fact that R(2ar, ar²) satisfies the equation of the normal:

a) Prove that p²+pr+2=0.

b) If the chord PR subtends a right angle at the vertex show that:
i. pr = -4
ii. p²=2

Thanks

 

[Beaconite]

sub R in the equation of normal

ii) use the fact m1 x m2 =-1 (for lines perpendicular)

 

[unity-]

sub R in the equation of normal

ii) use the fact m1 x m2 =-1 (for lines perpendicular)

a) been there, done that. Doesn't work.

 

[Beaconite]

a) been there, done that. Doesn't work.

use the fact that gradient of line p times gradient of normal = -1

or just wait, i 'll do it

 

[unity-]

use the fact that gradient of line p times gradient of normal = -1

or just wait, i 'll do it

im talking about part a!!!!!! i've subbed in R, and it doesn't work

 

[Beaconite]

ok find the gradient of PR and that shud be equal to -1/p (gradient of normal)

u get (p+r)/2 = - 1/p

and u end up getting p^2 + pr + 2=0

 

[unity-]

i've foudn the normal already

x +py = 2ap + ap^​3

 

[Beaconite]

i've foudn the normal already

x +py = 2ap + ap^​3

Bro u find the gradient of PR (line) which is the normal. Their gradients should be equal.

So Gradient of PR= gradient of normal

 

[unity-]

Bro u find the gradient of PR (line) which is the normal. Their gradients should be equal.

So Gradient of PR= gradient of normal

OMG SO SMART! thanks

 

[Beaconite]

OMG SO SMART! thanks

No worries

 

[Leffife]

OMG SO SMART! thanks

Thanks and you're welcome*

* = Good job Bacon

 

[Beaconite]

Thanks and you're welcome*

* = Good job Bacon

It's "beacon" not bacon m8 XD

 

[HeroicPandas]

It's "beacon" not bacon m8 XD

LOL