FP1 maths question help.

I'm stuck on a question about ellipses.
I've got an equation of an ellipse:

x^2/9 + y^2/25 = 1

Find the possible values of m for which the line y=mx+6 intersects the ellipse.

(edited 8 years ago)

Anyone?

I'm unsure if it is necessary, but I'd rewrite them to begin:

(x/3)^2 + (y/5)^2 = 1

Reply 3

zetamcfc

Original post by NeeIam

Anyone?

I am slightly confused (Perhaps because i've just got up) but you have the general equation of a line. Do you know what c is or not?

Reply 4

NeeIam

Original post by zetamcfc

I am slightly confused (Perhaps because i've just got up) but you have the general equation of a line. Do you know what c is or not?

Damn I should've proof read my initial post. The equation of the line is y=mx+6

Reply 5

AlmostNotable

Original post by NeeIam

I'm stuck on a question about ellipses.
I've got an equation of an ellipse:

x^2/9 + y^2/25 = 1

Find the possible values of m for which the line y=mx+6 intersects the ellipse.

Easiest way to solve this is to draw the ellipse then use trial and error to find m.

Reply 6

RoseGatz

Original post by NeeIam

I'm stuck on a question about ellipses.
I've got an equation of an ellipse:

x^2/9 + y^2/25 = 1

Find the possible values of m for which the line y=mx+6 intersects the ellipse.

Rewrite as:
(x/3)^2 + (y/5)^2 = 1

You know that the line y=mx+6 intersects the ellipse which implies that they share coordinates at least once, so plug in y=mx+6 into the rewritten version of the ellipse and expand. Once fully expanded, plug in the relevant values into b^2 - 4ac and then you should get the answer - hopefully.