Equation of the directrix of the parabola 4 y^2+12 x-12 y+39=0 is (a) x=(-7)/(4) (b) y=(3)/(4) (

step 1 So in this question equation of the directrix of this parabola is to be found We know that for t

Equation of the directrix of the parabola 4 y^2+12 x-12...

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Key Concepts

Completing the Square

Completing the square is an algebraic technique used to rewrite quadratic expressions in a form that easily reveals properties like vertex coordinates. This method is essential for converting the general equation of a parabola into its standard form to extract geometric features such as the vertex, focus, and directrix.

Parabola

A parabola is a type of conic section defined as the set of all points equidistant from a fixed point called the focus and a fixed line called the directrix. Its geometric properties and algebraic representation are fundamental in studying quadratic relations and conic sections.

Directrix

The directrix of a parabola is a fixed line used in its definition, such that each point on the parabola is equidistant from the focus and the directrix. Determining the directrix involves converting the given equation to a standard form that readily displays the distance relationships inherent to the parabola.

Standard Form of a Parabola

The standard form of a parabola is an algebraic representation that clearly shows its key features, including the vertex, axis of symmetry, focus, and directrix. Expressing a parabola in standard form allows one to apply geometric definitions directly and simplifies the process of analyzing its properties.

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