Latus Rectum (1 Viewer)

[GaDaMIt]

I dont get the basics.. what is it? why is it significant?

and furthermore a question involving it

Use the four standard forms to find the equation of the parabola with vertex at origin, axis vertical and:

e) equation of latus rectum y = 1

 

[Sober]

Latus rectum is a line that is parallel to the directorix and passes through the focus. I don't know what is meant by "four standard forms", but with the given information I can tell you that the focus is (0,1) so the porabola is x² = 4y

 

[pLuvia]

Latus rectum is just the line that passes through the focus of a curve.
So if the latus rectum is y=1, then the focus is (x,1). According to your equation the focus would be (0,1). Hence a=1, then the curve equation is x²=4y

 

[GaDaMIt]

okay .. last question of my h/w today.. doesnt really correlate with the title of this thread but didnt wanna create another..

The equation of a parabola is of the form y=kx^2. If the line 8x - y - 4 = 0 is a tangent to the parabola find the value of k

please show all working .. i dont know what to do ..

 

[pLuvia]

If that is a tangent, then the gradient of the curve should be the same as any point on the curve, i.e. the point where the tangent is created. Can you go from there?

 

[Sober]

Edit: pluvia and I keep posting at the same time, anyway here is an alternative way of solving it

The equation of a parabola is of the form y=kx^2. If the line 8x - y - 4 = 0 is a tangent to the parabola find the value of k

We have a curve and a line, if we simultaneously solve the two equations for x, then there should be exactly one solution since they intersect at only one point:

y = kx²
y = 8x-4

kx² = 8x-4
kx² - 8x + 4 = 0

For one solution the discriminant must be zero
discriminant = 64-16k = 0
k=4

 

[GaDaMIt]

If that is a tangent, then the gradient of the curve should be the same as any point on the curve, i.e. the point where the tangent is created. Can you go from there?

you mean differentiate the curve?

dy/dx = 2kx = 8

dunno what to do with the x..

thats IF thats what u meant..