he parabola x=y^2+ay+b crosses the parabola y=x^2 at (1,1) MAKING RIGHT ANGLES. WHAT ARE THE VALUES OF A AND B .
any help is greatly appreciated.
Since (1, 1) lies on $\displaystyle x=y^2+ay+b$ you know that
$\displaystyle a = -b$ .... (1)
To get another equation, I'd calculate the value of the gradient of the curves $\displaystyle x=y^2+ay+b$ and $\displaystyle y = x^2$ at (1, 1) and then set the product of the gradients equal to -1.
Now solve two equations simultaneously for a and b.