If `y=2x-3` is tangent to the parabola `y^2=4a(x-1/3),` then `a` is equal to

If y=2x+3 is a tangent to the parabola y^2=24 x , then find its distance from the parallel normal.

If y=m_1x+c and y=m_2x+c are two tangents to the parabola y^2+4a(x+a)=0 , then

The line 4x+2y = c is a tangent to the parabola y^(2) = 16x then c is :

If y+3=m_1(x+2) and y+3=m_2(x+2) are two tangents to the parabola y^2=8x , then

y=x is tangent to the parabola y=ax^(2)+c . If (1,1) is the point of contact, then a is

The line y = mx + 1 is a tangent to the parabola y^(2) = 4x if m = _____

The angle between the tangents to the parabola y^2=4a x at the points where it intersects with the line x-y-a=0 is (a) pi/3 (b) pi/4 (c) pi (d) pi/2

Statement 1: An equation of a common tangent to the parabola y^2=16sqrt(3)x and the ellipse 2x^2+""y^2=""4""i s""y""=""2x""+""2sqrt(3) . Statement 2: If the line y""=""m x""+(4sqrt(3))/m ,(m!=0) is a common tangent to the parabola y^2=""16sqrt(3)x and the ellipse 2x^2+""y^2=""4 , then m satisfies m^4+""2m^2=""24 . (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

If the tangents to the parabola y^2=4a x intersect the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at Aa n dB , then find the locus of the point of intersection of the tangents at Aa n dBdot

The point of intersection of the tangents of the parabola y^(2)=4x drawn at the end point of the chord x+y=2 lies on