Question

IF THE DISTANCE FROM THE FOCUS IS 2MM AND THE DISTANCE FROM THE DIRECTRIX IS 0.5MM,THEN WHAT IS THE NAME OF THE CONIC SECTION

Answer 1

If the distance from the focus is 2 mm and the distance from the directrix is 0.5 mm then what is the value of eccentricity? Explanation: Eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix and it is denoted by e. Therefore, by definition, e = 2 ÷ 0.5 = 4.

Answer 2

The name of the Conic Section is Hyperbola.

Explanation:

Given:

If the distance from the focus is 2 mm and the distance from the directrix is 0.5 mm.

To Find:

The name of the Conic Section.

Solution:

As given-If the distance from the focus is 2 mm and the distance from the directrix is 0.5 mm.

The distance from the focus=2mm.

The distance from the directrix =0.5mm

$Eccentricity (e) = \frac{The\ distance\ from\ the\ focus }{The \ distance\ from\ the\ directrix }$

                          $= \frac{2 }{0.5 }=4$

The value of eccentricity (e) is 4. The value of the eccentricity is greater than unity then the conic section is called as a hyperbola.

A hyperbola is the locus of all those points in a plane such that the difference in their distances from two fixed points in the plane is a constant.

Directrix of a hyperbola is a straight line that is used in generating a curve. It can also be defined as the line from which the hyperbola curves away from. This line is perpendicular to the axis of symmetry.

Thus, the name of the Conic Section is Hyperbola.

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