The discussion revolves around a problem involving a parabola defined by the equation y² = 4ax. Participants are tasked with showing a specific relationship between parameters p and q related to points on the parabola and the normals at those points.
The discussion is ongoing, with participants sharing their attempts and questioning the validity of their results. There is no clear consensus, but some guidance has been offered regarding the interpretation of the problem and the relationships between the variables.
Some participants express uncertainty about the accuracy of the problem statement and the derived coordinates, indicating potential issues with the original problem setup.
The expression is also dividable by q-p.sooyong94 said:Homework Statement
If the normal at P(ap^2 ,2ap) to the parabola y^2 = 4ax meets the curve again at Q(aq^2, 2aq), show that p^2 +pq+2=0
Homework Equations
Point-slope form
The Attempt at a Solution
I tried putting y=2aq and x=aq^2 but I can seem to simplify the whole thing other than dividing both sides by a
There should be minus in front of the last term in the first equation. You made a mistake when copying.sooyong94 said:Strangely enough I got this:
You have to work with x and y. What are p and q now?sooyong94 said:
Have you copied the question correctly? These x and y values do not fulfill the equation given y^2(x+2a)+4a^3 =0.sooyong94 said:
I mean the problem might be wrong. The coordinates of the point of intersection do not fit to the given locus.sooyong94 said: