if the parabola `y=x^2 + bx+c` touches the straight line` y=x` at (1,1)`, then `1000+100b+10c=`

If the parabola y=x^(2)+bx+c , touches the straight line x=y at the point (1,1) then the value of b+c is

Determine the parameters a,b,c in the equation of the parabola y = ax^(2) + bx + c so that it becomes tangent to the straight line y = x at the point x = 1 and passes through the point (-1,0).

If the parabolas y=x^(2)+ax+b and y=x(c-x) touch each other at the point (1,0), then a+b+c=

Let the parabolas y= x^(2)+ ax +b and y =x(c-x) touch cach other at point (1,0). Then

If the curve y=x^(2)+bx +c touches the line y = x at the point (1,1), then the set of values of x for which the curve has a negative gradient is

Let the parabolas y=x(c-x)and y=x^(2)+ax+b touch each other at the point (1,0), then-

Find the area bounded by the parabola y=x^(2)+1 and the straight line x+y=3

If the line y=mx+c touches the parabola y^(2)=4a(x+a) , then