Help!!! (1 Viewer)

[mazza_728]

One extremity of a focal chord in the parbol x^2=8y is t=3.
Find:
i) the gradient of the chord
As x^2 = 4ay
a=2
Also x=2at and y=at^2
Therefore x=12 and y=18
and focus = (0,2)
m=16/12
m=4/3
ii) the equation of the chord
y-y=m(x-x)
y-2=4/3(x-0)
3y-6=4x
4x-3y+6=0
iii) find cartesian co-ordinates of the other extremities of the chord.
I attempted to find point of intersection of x62=8y and 4x-3y+6=0 which i hoped would give me two points, one (12,18) which i already found and the other which would be the other extremity of the chord!
But on solving i found
x^2=8y
4x-3y+6=0
4x-24/x^2 + 6
4x^3+6x^2-24=0
2x^3+3x^2-12=0
Now my mind has either gone blank or i wouldnt have a clue how to solve the above equation.. can someone please help!! ASAP

 

[abdooooo!!!]

i have no idea what extremity is

i went through your working out. its all right until you attempted to find point of intersection of x^2=8y and 4x-3y+6=0.

you suppose to substitute y=x^2/8 into 4x-3y+6=0

which would give you: 3x^2 - 32x - 48 = 0

this is then solved by quadratics which should give you x = 12 or -4/3

so the two points are (12,18) and (-4/3,2/9)

 

[mazza_728]

thankyou! i realised that a few minutes after i posted - i always do stupid mistakes! i swear it will bring me down in maths

 

[abdooooo!!!]

try developing a systematic checking method if you have major problems with 'stupid' mistakes. like using a different method of mental calculation or use the calculator to confirm your answer.

also practice makes perfect... but there are other ways in which the speed and accuracy of your mathematics can be improved.

i believe there are 3 main reasons for some people to be better at math than others. they are:

1. amount of math done and the type of math that you do (although practicing any math will help out the other areas of math, you got to practice the type of math that is most relevant to what you want to be good at to maximise your marks)

2. the way you think (different systematic methods and strategies employed. like it would be impossible, even with practice, to calculate the product of 2 'five digit' numbers mentally in a few seconds if you were you using conventional methods)

3. size of the visual spatial brain/genetics (this is clearly demonstrated by the fact that most males are 'born' better than females in mathematics or math related subjects)

 

[Toodulu]

the extremity of a chord is just one of the ends (it lies on the parabola)