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Lesson Posted on 07 Feb Conic Sections

Raj Kumar

I am Six Sigma Black belt certified. I am 2011 pass out in B.tech from NIT Srinagar. I am an experienced,...

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

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Comments Lesson Posted on 07 Feb Conic Sections

Raj Kumar

I am Six Sigma Black belt certified. I am 2011 pass out in B.tech from NIT Srinagar. I am an experienced,...

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

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Comments Lesson Posted on 07 Feb Conic Sections

Raj Kumar

I am Six Sigma Black belt certified. I am 2011 pass out in B.tech from NIT Srinagar. I am an experienced,...

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 start with these 2 foci:

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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Comments Lesson Posted on 07 Feb Conic Sections

Raj Kumar

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

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Comments Lesson Posted on 06 Feb Conic Sections

Raj Kumar

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

Applying 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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Comments Lesson Posted on 03 Feb Conic Sections

Summary Of Circle & Relation With Conic section

Raj Kumar

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: x^{2} + y^{2} = r^{2}

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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Comments Lesson Posted on 03 Feb Conic Sections

Raj Kumar

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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Comments Lesson Posted on 03 Feb Conic Sections

Summary Of Straight Line & Relation With Conic Section

Raj Kumar

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 (x_{1}, y_{1}) with slope m

y − y_{1} = m(x − x_{1})

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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Comments Answered on 03/12/2016 Tuition/Class XI-XII Tuition (PUC) Tuition/Class XI-XII Tuition (PUC)/Mathematics Conic Sections

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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Answers 2 Comments Answered on 03/12/2016 Tuition/Class XI-XII Tuition (PUC) Tuition/Class XI-XII Tuition (PUC)/Mathematics Conic Sections

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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