Question

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

Solution

Correct option is

Parabola with its vertex at  and passing through 

Let the coordinates of P be (h, k)

Then 

⇒         h2 + k2 = (k + c)2

Locus of (h, k) is

                 

Which represents a parabola with vertex  and passing through .

SIMILAR QUESTIONS

Q1

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

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