# Co-odrinate geometry, deriving relationships between points

• Apr 13th 2010, 11:18 AM
AliceFisher
Co-odrinate geometry, deriving relationships between points
Well I've been doing okay working through my 1990 edition of Bostock and Chandler but have once more found a question I cannot fathom.

The point P(a,b) is equidistant from the y-axis and from the point (4,0). Find a relationship between a and b.

Now it seems to me that there will be a valid answer so long as a is greater than or equal to 2.

All of the other relationships so far have focused on the gradients of the lines in triangles and quadrilaterals.

Any push in the right direction would be appreciated.
• Apr 13th 2010, 11:36 AM
stapel
Hint: Look up the classical definition of the conic called a "parabola". (Wink)

Definition
• Apr 13th 2010, 11:45 AM
Quote:

Originally Posted by AliceFisher
Well I've been doing okay working through my 1990 edition of Bostock and Chandler but have once more found a question I cannot fathom.

The point P(a,b) is equidistant from the y-axis and from the point (4,0). Find a relationship between a and b.

Now it seems to me that there will be a valid answer so long as a is greater than or equal to 2.

All of the other relationships so far have focused on the gradients of the lines in triangles and quadrilaterals.

Any push in the right direction would be appreciated.

Hi Alice,

if (4,0) is the focus of a parabolic curve that crosses the x-axis at (2,0)
and opens out above and below the x-axis in the positive x-direction,
what can we then say about the horizontal distance from the y-axis to
a point on the curve and the distance from (4,0) to the same point on the curve?

Hence

$(a-4)^2+b^2=a^2$
• Apr 13th 2010, 11:59 AM
AliceFisher
My thanks to both of you, the parabola was the image I has in my mind even if I did not know what it was called or how to use it.

I also don't feel so bad about not being able to answer the question since the book I am using does not actually introduce the concept for another 6 chapters!

The good news is I was able to follow both the site (stapel) and from there your definition Archie.

One more gap in my knowledge soundly plugged!