Line y=2x-b cuts the parabola `y=x^(2)-4x` at points A and B. Then the value of b for which `angleAOB` is a right is (where O is origin) _________ .

Answer

7

Explanation

(7) The line is y=2x-b,i.e.,
`1=(2x-y)/(b)`
Homogenizing parabola with line, we get
`x^(2)-4x((2x-y)/(b))-y((2x-y)/(b))=0`
Since `angleAOB=90^(@)`
Coefficient of `x^(2)+"coefficient of "y^(2)=0`
`or1-(8)/(b)+(1)/(b)=0`
`orb=7`