Find the point on the parabola `y^(2) = 2x` that is closest to the point (1, 4)

Find a point on the parabola y^(2) = 2 that is closest to the point (1, 32)

Find the locus of the midpoint of chords of the parabola y^2=4a x that pass through the point (3a ,a)dot

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

Find the equation of tangents of the parabola y^2=12 x , which passes through the point (2, 5).

(i) Find the points of intersection of the parabola y ^(2) = 8x and the line y = 2x . (ii) Find, using integration, the area enclosed between the line and the parabola.

The area (in sq units) of the smaller of the two circles that touch the parabola, y^(2) = 4x at the point (1,2) and the X-axis is

Find the coordinates of a point the parabola y^(2)=8x whose distance from the focus is 10.

Find the coordinates of points on the parabola y^2=8x whose focal distance is 4.

Find the equations of the tangent and normal to the parabola y^(2) = 4ax at the point (at^(2) , 2at).

Find the equation of the tangent to the parabola y^2=8x having slope 2 and also find the point of contact.