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

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

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.

If the line 2x+sqrt6y=2 touches the hyperbola x^2-2y^2=4 , then the point of contact is

If the line x+y=6 is a normal to the parabola y^(2)=8x at point (a,b), then the value of a+b is ___________ .

The common tangents to the circle x^2 + y^2 =2 and the parabola y^2 = 8x touch the circle at P,Q andthe parabola at R,S . Then area of quadrilateral PQRS is

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

Show that the line x + y + 1=0 touches the hyperbola x^(2)/16 -y^(2)/15 = 1 and find the co-ordinates of the point of contact.

If the line x+y=a touches the parabola y=x-x^2, 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