Question

Shortest distance of the point (0, c) from the parabola y = x2where  is

Solution

Correct option is

It is the distance of the point (x, y) on the parabola y = x2 from

(0, c). then

                    …. (1)

Which is least ⇒ S2 is least

       

When x = 0, S = c, when 

And .

Hence the least distance is

SIMILAR QUESTIONS

Q1

A point P moves such that the difference between its distance from the origin and from the axis of x is always a constant c. the locus of P is a

Q2

The length of the intercept on the normal at the point (at2, 2at) of the parabola y2 = 4ax made by the circle which is described on the focal distance of the given point as diameter is 

Q3

A line bisecting the ordinate PN of a point P(at2, 2at), t > 0, on the parabola y2 = 4ax is drawn parallel to the axis to meet the curve at Q. If NQ meets the tangent at the vertex at the point T, then the coordinates of T are.

Q4

If P, Q, R are three points on a parabola y2 = 4ax whose ordinates are in geometrical progression, then the tangents at and R meet on

Q5

If Land L2 are the length of the segments of any focal chord of the parabola y2 = x, then  is equal to