Prove that the straight line x+ y = 1 touches the parabola `y= x-x^2`

Prove that the line x/l+y/m=1 touches the parabola y^2=4a(x+b) , if m^2(l+b)+al^2=0 .

Find the angles at which the following lines intersect: (a) the straight line y = 4 - x and the parabola y = 4-(x^(2))/(2) (b) the sinusoid y = sin x and the cosine curve y = cos x

Statement I Straight line x+y=lamda touch the parabola y=x-x^2 , if k=1. Statement II Discriminant of (x-1)^2=x-x^2 is zero.

The straight line y+x=1 touches the parabola (A) x^(2)+4y=0 (D) x^(2)-x+y=0 (C) 4x^(2)-3x+y=0( D ) x^(2)-2x+2y=0

The straight line y=mx+c , (m > 0) touches the parabola y^(2)=8(x+2) then the minimum value taken by c is

Area of the parabolic segment cut by the straight line y = 2 x + 3 off the parabola y = x^(2) is

Prove that the straight line y=x+sqrt((7)/(12)) touches the ellipse.3x^(2)+4y^(2)=1

The line x+y+1=0touches the parabola y^2=kx if k=_____.

The number of values of c such that the straight line y=4x+c touches the curve (x^(2))/(4)+y^(2)=1 is k then, k is