Find the point of intersection of the curves `y= 2x^2-x+1` and `y=3x+4` whose slopes of tangents are equal.

Answer

4

Explanation

4
We have parabola `y^(2)=8x` with circle `x^(2)+y^(2)-2x-4y=0`
Solving parabola `(2t^(2),4t)` with circle, we get
`4t^(4)+16t^(2)-4t^(2)-16t=0`
`ort^(4)+3t^(2)-4t=0`
`rArrt=0,1`
So, the point and Q are (0,0) and (2,4), respectively which are also diameterically opposite points on the circle . The focus is S(2,0).
`"Area of "DeltaPQS=(1)/(2)xx2xx4=4` sq. units