Locus and the Parabola Questions (1 Viewer)

[Carl5]

I'm having a few difficulties, as usual lol.

1.
From which point on the parabola x^2=4ay does the normal pass through the focus?

I know it's at 0,0 just by look at the question, but how do I work this out?


2.
Find the equation of the parabola with axis parallel to the y -axis and passing through points (0,-2), (1,0) and (3,-8)



I'll probably have more questions tomorrow.

Thanks in advance!

 

[bored of fail 1]

Q2.

is real easy , just 3 simultaneous eqns in 3 unknowns

 

[bored of fail 1]

1. is also easy

dy/dx = x/ 2a

now consider a point (b , c)

when x=b, grad of tangent= b/(2a) therefore grad of normal = -2a / b

therefore the eqn of the normal is y -c = (-2a/b) ( x-b )

but this must pass through the focus ( which is (0,a) ) , therefore (0,a) satifies the eqn

so sub in a -c = [-2a/ b] (0-b)

so a - c = 2a , so a=-c

EDIT: mm there is a problem if b=0 , because we then divide by 0 in expression -2a/b , so im fairly sure there is only a geometric soln to it.

 

[blackops23]

1. is also easy

dy/dx = x/ 2a

now consider a point (b , c)

when x=b, grad of tangent= b/(2a) therefore grad of normal = -2a / b

therefore the eqn of the normal is y -c = (-2a/b) ( x-b )

but this must pass through the focus ( which is (0,a) ) , therefore (0,a) satifies the eqn

so sub in a -c = [-2a/ b] (0-b)

so a - c = 2a , so a=-c

EDIT: mm there is a problem if b=0 , because we then divide by 0 in expression -2a/b , so im fairly sure there is only a geometric soln to it.

you're not bored of fail 3, are you? bloody poser

 

[bored of fail 1]

you're not bored of fail 3, are you? bloody poser

of course I am, who else is genius enough / cares enough to answer maths questions on here.

all my other accounts are banned

 

[Carl5]

Ok, I must have mistakes in my algebra for question 2.

Could someone provide the working out for me. I keep stuffing up...

And how do I work out question 1 from a = -c? I'm not sure where to go with it.

 

[Aindan]

2.
Find the equation of the parabola with axis parallel to the y -axis and passing through points (0,-2), (1,0) and (3,-8)

uh...why don't you try plotting the points on a number plane. Is it even possible for a parabola to be made that its axis is parallel to y axis......

 

[Bored Of Fail]

2.
Find the equation of the parabola with axis parallel to the y -axis and passing through points (0,-2), (1,0) and (3,-8)

uh...why don't you try plotting the points on a number plane. Is it even possible for a parabola to be made that its axis is parallel to y axis......

consider the general parabola, y=ax^2 +bx +c

then you have three points on the parabola, so they satisfy the eqn. then solve the three simultaneous eqns to find the coefficents