1. ## Finding the locus

Hi

For the question:

P is a variable on the curve y = 2x^2 + 3 and O is the origin. Q is the point of the section of OP nearer the origin. Find the locus of Q.

After I find Q = (2x/3,2y/3) from the ratio formula, what do i do to find the locus?

2. Originally Posted by xwrathbringerx
Hi

For the question:

P is a variable on the curve y = 2x^2 + 3 and O is the origin. Q is the point of the section of OP nearer the origin. Find the locus of Q.

After I find Q = (2x/3,2y/3) from the ratio formula, what do i do to find the locus?
What do you mean by "the point on the section of OP nearer the origin"? Nearer the origin than what? What do you mean by "section of OP"? OP normally means "the line segment from O to P" and that includes O itself.

What, exactly, did you do to find Q= (2x/3, 2y/3)? For that matter, what does it mean? Is the "y" in that given by y= 2x^2+ 3? If so, then (2x/3, 2y/3)= (2x/3, 4x^2/3+ 2). Now, let u= 2x/3 so that x= 3u/2. Putting that into y= 4x^2/3+ 2 gives y= 4(9u^2/4)+ 2= 9u^2+ 2 or (u, 9u^2+2). That gives y= 9x^2+ 2 as the locus.

3. Originally Posted by HallsofIvy
What do you mean by "the point on the section of OP nearer the origin"? Nearer the origin than what? What do you mean by "section of OP"? OP normally means "the line segment from O to P" and that includes O itself.

What, exactly, did you do to find Q= (2x/3, 2y/3)? For that matter, what does it mean? Is the "y" in that given by y= 2x^2+ 3? If so, then (2x/3, 2y/3)= (2x/3, 4x^2/3+ 2). Now, let u= 2x/3 so that x= 3u/2. Putting that into y= 4x^2/3+ 2 gives y= 4(9u^2/4)+ 2= 9u^2+ 2 or (u, 9u^2+2). That gives y= 9x^2+ 2 as the locus.
I'm so sorry....

I meant:

P is a variable on the curve y = 2x^2 + 3 and O is the origin. Q is the point of trisection of OP nearer the origin. Find the locus of Q

4. Hi

That's more clear now

You have found $x_Q = \frac{x}{3}$ and $y_Q = \frac{y}{3} = \frac23x^2 + 1$

To find the locus of Q you need to find a relationship between $x_Q$ and $y_Q$