Why is this solution incorrect?
Prove that on the axis of any parabola there is a certain point K which has the property that, if a chord PQ of the parabola be drawn through it, then is the same for all positions of the chord.
If it would be valid for standard parabola than it would be valid for all parabolas. Thus, proving for .
let the point K be (c,0)
Equation of line PQ using parametric coordinates: (Equation 1), (Equation 2)
From equation 1 and 2: (Equation 3)
Using Equation 3 and , we get this quadratic in r: (Equation 4)
Roots of this quadratic would be the lengths of PK and QK
From Equation 4, and
As value of is not constant thus does not turn out to be constant. Hence, this solution is incorrect.
I've seen the correct solution but I wanted to know why this solution is incorrect?