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What is the locus of a point which moves on a plane such that its distance from a fixed point is always equal to its distance from a fixed line? – 2017

what is the locus of a point which moves on a plane such that its distance from a fixed point is always equal to its distance from a fixed line?

A chord passing through the focus and perpendicular to the axis of the conic is called latus rectum. The locus of a point which moves in a plane such that it’s distance from a fixed point focus is always equal to it’s distance from a fixed line directrix in the same plane.

An ellipse is the locus of a point in a plane which moves in the plane in such a way that the ratio of its distance from a fixed point (called focus) in the same plane to its distance from a fixed straight line (called directrix) is always constant which is always less than unity.

The constant ratio usually denoted by e (0 < e < 1) and is known as the eccentricity of the ellipse.
If S is the focus, ZZ' is the directrix and P is any point on the ellipse, then by definition
SPPMSPPM = e
⇒ SP = e ∙ PM
The fixed point S is called a Focus and the fixed straight line L the corresponding Directrix and the constant ratio is called the Eccentricity of the ellipse.