ATMIYA INSTITUTE OF ATMIYA INSTITUTE OF TECHNOLOGY AND SCIENCETECHNOLOGY AND SCIENCENAME :- BHAUTIK VACHHANI NAME :- BHAUTIK VACHHANI DIVISON :- GZ -1 DIVISON :- GZ -1 BRANCH :- CIVIL BRANCH :- CIVIL ENGINEERINGENGINEERINGSUBJECT:- ENGINEERING SUBJECT:- ENGINEERING GRAPHICS GRAPHICS

CONICS CONICS & &

INVOLUTE INVOLUTE

CLASSIFICATION

CONIC INVOLUTE

1. CIRCLE2. ELLIPSE3. PARABOLA4. HYPERBOLA5. RECTANGULAR HYPERBOLA

1.Circle

2.polygon

CONICS

The curves obtained by the intersection of a cone by cutting plane in different positions are called conics.

The conics are1.CIRCLE2.ELLIPSE3.PARABOLA4.HYPERBOLA5.RECTANGULAR

HYPERBOLA

DEFINING CONICSCurve Position of Cutting Plane

Circle Perpendicular to axis and parallel to the base

Ellipse Inclined to the axis and not parallel to any generator. Angle of Cutting Plane > Angle of Generator

Parabola Inclined to axis, parallel to generators and passes through the base and axis

Hyperbola Inclined to the axis and not parallel to any generator. Angle of Cutting Plane < Angle of Generator

Rectangular Hyperbola Parallel to the Axis and

Perpendicular to the Base

ELLIPSE

Ellipse is defined as the locus of points the sum of whose distances from two fixed points, called the foci, is a constant.

PARABOLA

Parabola is defined as the locus of points whose distances from a fixed point, called the focus, and a fixed line, called the directrix, are always equal.

HYPERBOLA

Hyperbola is defined as the locus of points whose distances from two fixed points, called the foci, remains constant.

INVOLUTES

> An involutes is a curve traced by a point as it unwinds from around a circle or polygon.

>The concerned circle or polygon is called as Involutes.

circle

Polygon-1

Polygon - 2

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