The maximum number of points on the parabola will be obtained when they are intersection point with a circle.
A circle can intersect a parabola at maximum $4$ points

Question

The maximum number of points on the parabola y2=16x which are equidistant from a variable point P (which lie inside the parabola) are (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

The maximum number of points on the parabola will be obtained when they are intersection point with a circle. A circle can intersect a parabola at maximum 4 points <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-ms7kxy505jri.png" />

Q. The maximum number of points on the parabola y2=16x which are equidistant from a variable point P (which lie inside the parabola) are

The maximum number of points on the parabola will be obtained when they are intersection point with a circle. A circle can intersect a parabola at maximum 4 points

Q. The maximum number of points on the parabola $y^{2} = 16 x$ which are equidistant from a variable point $P$ (which lie inside the parabola) are

The maximum number of points on the parabola will be obtained when they are intersection point with a circle.
A circle can intersect a parabola at maximum $4$ points