Locus Question (1 Viewer)

[Smile12345]

Hello All...

It's a bit of a dumb question. But appreciate any/all help.

Q(2aq, aq^2) lies on the parabola x^2 = 4ay.

Find the equation of the focal chord through Q.
Prove that the length of the latus rectum is 4a.

Thanks.

 

[cookiez69]

a = 3/4 units
F(0, 3/4)

m = (3-3/4) / (-3-0)
m = -3/4

Sub into the point gradient formula
y - 3 = -3/4 . (x+3)
4y-12 = -3x - 9
3x + 4y - 3 = 0

 

[Smile12345]

Thanks heaps Cookiez69...

 

[Smile12345]

Part C of this question... Find the coordinates of the point R where the line PF meets the directrix.

Thanks in advance.

 

[Smile12345]

Another Question.... It's a bit of a dumb question. But appreciate any/all help.

Q(2aq, aq^2) lies on the parabola x^2 = 4ay.

Find the equation of the focal chord through Q.
Prove that the length of the latus rectum is 4a.

Thanks.

 

[Smile12345]

Can someone please help me?

 

[cookiez69]

Part C of this question... Find the coordinates of the point R where the line PF meets the directrix.

Thanks in advance.

D: y = -3/4

Sub y = -3/4 into the equation of the line PF.

3x + 4(-3/4) - 3 = 0
3x - 6 = 0
x = 2

Therefore R(2,-3/4)

 

[Smile12345]

D: y = -3/4

Sub y = -3/4 into the equation of the line PF.

3x + 4(-3/4) - 3 = 0
3x - 6 = 0
x = 2

Therefore R(2,-3/4)

Yup, I get yah... Thanks heaps.