Math Is Fun Forum

Au101

Member

Registered: 2010-12-01

Posts: 353

Coordinate Systems (parabolas)

Hi guys,

I'm a bit stuck on this question on coordinate systems:

I don't know where to go for part (b).

Any ideas?

Thanks

Last edited by Au101 (2011-04-07 05:31:38)

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Coordinate Systems (parabolas)

Hi Au101,

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Coordinate Systems (parabolas)

Oh okay, thanks gAr. This is what confused me, because that is, of course, the equation of the tangent to C at P. What I don't understand is why that passes through the point of intersection of the tangents to C at A and B.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Coordinate Systems (parabolas)

Hi Au101;

Sorry, could not get to you, very busy in here and it is only me right now. What about gAr's answer are you having problems with?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Coordinate Systems (parabolas)

Oh no not at all bobbym. Well, the way I see it is we have a parabola and I've found the equation of some tangent to that parabola at a point P with the coordinates given in the question. I also have the coordinates of the point of intersection of two separate tangents to the parabola, at the points A and B. Now, it seems to me that gAr's answer rests on the assumption that this point of intersection also lies on the tangent to the parabola at P. But I don't see why that is implied.

Last edited by Au101 (2011-04-07 09:21:09)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Coordinate Systems (parabolas)

The point of intersection does not lie on the parabola but somewhere outside of it. Why do you think that it is on the parabola? Can you be specific.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Coordinate Systems (parabolas)

Okay, well, if we begin with the first line,

Have I, then, misunderstood.

Is the equation of the tangent to the parabola at P. Why, then, can I substitute in the point of intersection of the other two tangents, I don't understand.

Thanks

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Coordinate Systems (parabolas)

Hi Au101;

I am sorry, I am drawing a blank on it right now. I will post if I get something.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Coordinate Systems (parabolas)

Well, I suppose, this is what one gets if one teaches oneself a topic several months before attempting relevant exercises. As has now been pointed out to me by a friend of mine, the point P is a general point on the parabola, and hence that equation of the tangent to C at P is that of a general tangent. Thank you so much to both of you for your trouble :)

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Coordinate Systems (parabolas)

Hi Au101,

Glad that you got it, you're welcome!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."