The focal distance of a point on the parabola y^2=12 x is 4 . Then the abscissa of this point is

step 1 In this question it is given that the focal distance of a point on the parabola y square equals

The focal distance of a point on the parabola y^2=12 x is 4...

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Key Concepts

Algebraic Substitution in Coordinate Geometry

This concept involves substituting expressions from one equation (like the equation of a conic) into another equation, such as a distance formula. It allows for the elimination of variables and the reduction of a geometric problem to an algebraic one that can be solved for unknown coordinates.

Focal Distance

The focal distance refers to the distance between any point on a parabola and its focus. This distance is found using the distance formula and is key to problems where the relationship between the point and the focus is given or needs to be determined.

Focus of a Parabola

For a parabola expressed as y² = 4ax, the focus is located at (a, 0). The focus is a central feature from which many properties of the parabola are derived, such as the reflective property and the definition of distances used in the conic section.

Standard Form of a Parabola

A parabola with a horizontal axis is typically written in the form y² = 4ax, where 'a' is a parameter that determines the distance from the vertex to the focus. This form conveys essential information about the parabola's geometry and makes further calculations involving the focus and directrix straightforward.

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