If the line x+y=a touches the parabola y...

If the line `x+y=a` touches the parabola `y=x-x^2,` then find the value of `adot`

Verified by Experts

The correct Answer is:

a=1

Eliminating y, we have
`a-x=x-x^(2)orx^(2)-2x+a=0`
Since the touches the parabola, we must have equal roots.
Therefore,
4-4a=0 or a=1

Similar Questions

Explore conceptually related problems

If y=x+2 is normal to the parabola y^2=4a x , then find the value of adot

If the chord of contact of tangents from a point P to the parabola y^2=4a x touches the parabola x^2=4b y , then find the locus of Pdot

If the line y = 3x + 1, touches the parabola y^(2) = 4ax , find the length of the latus rectum ?

If the line y=3x+c touches the parabola y^2=12 x at point P , then find the equation of the tangent at point Q where P Q is a focal chord.

The line x - y + 2 = 0 touches the parabola y^2 = 8x at the point

Prove that the line 5x+12y=9 touches the hyperbola x^(2)-9y^(2)=9 and find the point of contact.

If the point P(a^2,a) lies in the region corresponding to the acute angle between the lines 2y=x and 4y=x , then find the values of adot

The axis of the parabola y^2 = x is the line

If line 3x-a y-1=0 is parallel to the line (a+2)x-y+3=0 then find the value of adot

Statement 1: The line y=x+2a touches the parabola y^2=4a(x+a) Statement 2: The line y=m x+a m+a/m touches y^2=4a(x+a) for all real values of mdot