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FP1 Edexcel Practice Paper D Q9

Hi there,

I am a gap year student and so have no support from a teacher.

I have a problem with part D:

9. The point P(ap2, 2ap) lies on the parabola M with equation y2 = 4ax, where a is a positive constant.
(a) Showthatanequationofthetangent to M at P is py = x + ap2.
The point Q(16ap2, 8ap) also lies on M.
(b) Writedownanequationofthetangent to M at Q.
The tangent at P and the tangent at Q intersect at the point V.
(c) Show that, as p varies, the locus of V is a parabola N with equation
4y^2 = 25ax.
(d) FindthecoordinatesofthefocusofN,andfindanequationofthedirectrixofN.
(e) Sketch M and N on the same diagram, labelling each of them.

Given the equation of the locus of V, how can you find the focus and directrix equation?

Thanks for any help in advance!

Reply 1

Alpha95

Original post by usycool1

You should know that the general equation of a parabola is y^2 = 4ax, and that the focus is at (a, 0) and the directerix is at x = -a (If you don't get why, have a look at your textbook/notes.). It should be fairly easy to do once you recall this.

I know those things, but don't see how I should utilise the information?

The answer is (25a/16, 0) etc.

(edited 10 years ago)

Reply 2

davros

Original post by kelsey.phillips

I know those things, but don't see how I should utilise the information?

The answer is (25a/16, 0) etc.

Have you not done part (c)?

Once you have the locus you just need to rearrange it into the form y^2 = 4Ax for suitable A then you can read off the focus and directrix properties.

Reply 3

Alpha95

Original post by davros

Have you not done part (c)?

Once you have the locus you just need to rearrange it into the form y^2 = 4Ax for suitable A then you can read off the focus and directrix properties.

Yeah I did do part C :s-smilie:

I think I must be completely missing the point haha
So we have 4y^2 = 25ax.
y^2 = (25/4)ax.

But that doesn't give the answer?? My brain must be jumbled?

Reply 4

davros

Original post by kelsey.phillips

Yeah I did do part C :s-smilie:

I think I must be completely missing the point haha
So we have 4y^2 = 25ax.
y^2 = (25/4)ax.

But that doesn't give the answer?? My brain must be jumbled?