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Lesson Posted on 07/02/2018 Conic Sections

Raj Kumar

I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...

Why study ellipses? Orbiting satellites (including the earth revolving around the sun, and the moon revolving around us) trace out elliptical path. Many buildings and bridges use the ellipse as a pleasing (and strong) shape. One... read more

#### One property of ellipses is that a sound (or any radiation) beginning in one focus of the ellipse will be reflected so it can be heard clearly at the other focus.

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Lesson Posted on 07/02/2018 Conic Sections

Raj Kumar

I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...

Ellipses with Horizontal Major Axis: Equation for an ellipse with a horizontal major axis is given by: read more

## Equation for an ellipse with a horizontal major axis is given by:

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Lesson Posted on 07/02/2018 Conic Sections

Raj Kumar

I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...

The ellipse is defined as the locus of a point (x,y) which moves so that the sum of its distances from two fixed points (called foci, or focuses) is constant. We can produce an ellipse by pinning the ends of a piece of string and keeping a pencil tightly within the boundary of the string, as follows. We... read more

The ellipse is defined as the locus of a point (x,y) which moves so that the sum of its distances from two fixed points (called foci, or focuses) is constant.

We can produce an ellipse by pinning the ends of a piece of string and keeping a pencil tightly within the boundary of the string, as follows.

We pin the ends of the string to the foci and begin to draw, holding the string tight:

Our complete ellipse is formed:

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Lesson Posted on 07/02/2018 Conic Sections

Raj Kumar

I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...

A hyperbola is a pair of symmetrical open curves. It is what we get when we slice a pair of vertical joined cones with a vertical plane. How can we obtain a hyperbola from slicing a cone? We start with a double cone (2 right circular cones placed apex to apex): ... read more

#### The curve that results is called a hyperbola. There are two parts to the curve.

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Lesson Posted on 06/02/2018 Conic Sections

Raj Kumar

I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...

A hyperbola is a pair of symmetrical open curves. It is what we get when we slice a pair of vertical joined cones with a vertical plane. How do we create a hyperbola? Take 2 fixed points A and B and let them be 4a units apart. Now, take half of that distance (i.e. 2a units). Now, move along a curve... read more

#### b2 = c2 − a2Applying the distance formula for the general case, in a similar fashion to the above example, we obtain the general form for a north-south hyperbola:    y2/a2-x2/b2 = 1

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Lesson Posted on 03/02/2018 Conic Sections

Raj Kumar

I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...

1. Slope-Intercept form: Y=mx+b 2. Point-slope form: The equation of a line passing through a point (x1, y1) with slope m y − y1 = m(x −... read more

1. Slope-Intercept form:

Y=mx+b

2. Point-slope form:

The equation of a line passing through a point (x1, y1) with slope m

y − y1 = m(x − x1)

Genreral Form of Straight line is given by:

Ax+By+C=0

Conic Section:

If we slice the double cone by a plane just touching one edge of the double cone, the intersection is a straight line, as shown above.

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Lesson Posted on 03/02/2018 Conic Sections

Raj Kumar

I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...

If we slice one of the cones with a plane at right angles to the axis of the cone, the shape formed is a circle. The circle with centre (0, 0) and radius r has the equation: x2 + y2... read more

If we slice one of the cones with a plane at right angles to the axis of the cone, the shape formed is a circle.

The circle with centre (0, 0) and radius r has the equation: x2 + y2 = r2

The circle with centre (h, k) and radius r has the equation: (x − h)2 + (y − k)2 = r2

General Form of the Circle: An equation which can be written in the following form (with constants D, E, F) represents a circle: x2 + y2 + Dx + Ey + F = 0x2 + y2 + 2gx + 2fy + c = 0Radius=√g2+f2-ccenter of Circle is given by: -g,-f

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Lesson Posted on 03/02/2018 Conic Sections

Raj Kumar

I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...

The set of all points that share a property. This usually results in a curve or surface. Example: Circle: A Circle is "the locus of points on a plane that are a certain distance from a central point". A circle is the locus of points that are equidistant... read more

The set of all points that share a property. This usually results in a curve or surface.

Example:

Circle:

• A Circle is "the locus of points on a plane that are a certain distance from a central point".
• A circle is the locus of points that are equidistant from a fixed point (the center).

Parabola:

• A parabola is the locus of points that are equidistant from a point (the focus) and a line (the directrix).

Ellipse:

•  An ellipse is the locus of points whereby the sum of the distances from 2 fixed points (the foci) is constant.
Hyperbola:

• A hyperbola is the locus of points where the difference in the distance to two fixed foci is constant.

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Show that the point (5, 6) outside the circle: (square of x) + (square of y) = 4?

Sarvajeet Kumar

An Experienced Trainer

S'=(square of 5) + (square of 6) - 4 = -57.
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Find the equation of the circle which passes through the points (1, 2), (2, 2) and (4, -1)?

Sarvajeet Kumar

An Experienced Trainer

square of (x-3/2) + square of (y-3/2) = 1/2.
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