At what point on the parabola `y^2=4x` the normal makes equal angle with the axes? (A) `(4,4)` (B) `(9,6)` (C) `(4,-4)` (D) `(1,+-2)`

Find the points on the parabola y^2-2y-4x=0 whose focal length is 6.

The vertex of the parabola y^2 = 4x + 4y is

At what point of curve y=2/3x^3+1/2x^2, the tangent makes equal angle with the axis? (a) (1/2,2/(24))a n d(-1,-1/6) (b) (1/2,4/9)a n d(-1,0) (c) (1/3,1/7)a n d(-3,1/2) (d) (1/3,4/(47))a n d(-1,-1/3)

A normal chord of the parabola y^2=4ax subtends a right angle at the vertex if its slope is

The coordinates of a point on the parabola y^2=8x whose distance from the circle x^2+(y+6)^2=1 is minimum is (2,4) (b) (2,-4) (18 ,-12) (d) (8,8)

From the point (15, 12), three normals are drawn to the parabola y^2=4x . Then centroid and triangle formed by three co-normals points is (A) ((16)/3,0) (B) (4,0) (C) ((26)/3,0) (D) (6,0)

If the normal chhord of the parabola y^(2)=4x makes an angle 45^(@) with the axis of the parabola, then its length, is

if the normal at the point t_(1) on the parabola y^(2) = 4ax meets the parabola again in the point t_(2) then prove that t_(2) = - ( t_(1) + 2/t_(1))

The mirror image of the parabola y^2=4x in the tangent to the parabola at the point (1, 2) is (a) (x-1)^2=4(y+1) (b) (x+1)^2=4(y+1) (c) (x+1)^2=4(y-1) (d) (x-1)^2=4(y-1)

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