The directrix and focus are different distances from a given point on a parabola is false statement.
What is directrix ?
Directrix is a line. Directrix is a straight line distance to which from any point of a conic section is in fixed ratio to the distance from the same point to a focus. The directrix is perpendicular to the axis of symmetry and does not touch the parabola.
What is focus ?
Focus is a point. Focus in Parabola is a set of points in the plane which are at equal distance from the given point and line. This point is known as the focus of the parabola and the line is called the directrix. It lies on the axis.
So, from the above mentioned definitions of directrix and focus, we can say that the given statement in the question is false.
Hence, we can say that the directrix and focus are different distances from a given point on a parabola is false statement.
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