Find the point on the curve `y^2=4x` which is nearest to the point (2, 1).

Find the point on the curve x^2=8y which is nearest to the point (2,\ 4) .

Find the point P on the curve y^(2)= 4ax which is nearest to the point (11a, 0)

Determine the points on the curve x^2=4y which are nearest to the point (0,5).

Equation of normal to parabola y^2 = 4ax at (at^2, 2at) is y-2at = -t(x-at^2) i.e. y=-tx+2at + at^3 Greatest and least distances between two curves occur along their common normals. Least and greatest distances of a point from a curve occur along the normal to the curve passing through that point. Now answer the following questons: The point on the parabola y^2 = 4x which is nearest to the point (2, 1) is: (A) (1,2) (B) (1,2sqrt(2) (C) (1, -2) (D) none of these

Find the point on the curve 3x^2-4y^2=72 which is nearest to the line 3x+2y+1=0.

The point on the curve x^2=2y which is nearest to the point (0, 5) is(A) (2sqrt(2),4) (B) (2sqrt(2),0) (C) (0, 0) (D) (2, 2)

The ordinate of point on the curve y =sqrtx which is closest to the point (2, 1) is

Distance of point P on the curve y=x^(3//2) which is nearest to the point M (4, 0) from origin is

Find the equation of the normal to the curve x^2=4y which passes through the point (1, 2).

Find the point on the curve y^2=2x which is at a minimum distance from the point (1,\ 4) .