Points of Intersection
Example Question 1
- \(x=4at^2\)
- \(y=a(2t-1)\)
- Passes through (4,0)
- \(a(2t-1)=0\)
- \(2ta-a=0\)
- \(2ta=a\)
- \(2t=1\)
- \(t=\frac{1}{2}\)
- \(4\times a\times\frac{1}{2}^2\)
- \(4\times\frac{1}{4}\times a=4\)
- \(a=4\)
Find where \(x=t^2\), \(y=2t\) intercepts \(x^2+y^2-9x+4=0\)
- \(t^4+4t^2-9t^2+4=0\)
- \(t^4-5t^2+4=0\)
- \(t=^+_{-}2, ^+_{-}1\)
- Co-ordinates are \((4, 4), (4, -4), (1, 2), (1,-2)\)