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Conic Sections Defination:

A conic section is a curve formed by the intersection of a cone's surface with a plane in mathematics.The hyperbola, parabola, and ellipse are the three forms of conic sections; the circle is a special case of the ellipse, but it was previously referred to be a fourth.

 

Top things to learn under Conic Sections from the online tutor

 

The closest thing that you can relate to conic sections is the ice-cream cone you recently had. Do you remember how it looked? 


It was an intersection of the surface of a cone with a plane. Apart from that, there are three more types- the ellipse, the hyperbola, and the parabola.


By attending an online class with us, you will gain an in-depth understanding of-
 

  • Eccentricity, focus, and directrix
  • Conic parameters
  • Cartesian coordinates
  • Polar coordinates
  • Applications of Conic Sections

 

Conic Sections Frequently Asked Questions:

Question 1: What are conic sections?

In geometry, a conic section is any curve formed by the intersection of a plane with a right circular cone.

The intersection is a circle, an ellipse, a hyperbola, or a parabola, depending on the angle of the plane relative to the cone.

 

Question 2: How to graph conic sections?

 

The collection of locations P whose distance from the focus is a constant multiple of the distance from P to the conic's directrix is known as a conic section.On a coordinate plane, a conic section can be graphed.Every conic section has specific characteristics, such as a focus and a directrix.


Parabolas have a single focus and directrix, whereas ellipses and hyperbolas have two.

 

Question 3: How to identify conic sections?

 

To make a conic, an equation must include x^2 and/or y^2.


A conic section's variables cannot be increased by more than one or two powers. Each sort of conic has its own set of features.


The x^2 and y^2 terms must be on the same side of the equal sign in order for their qualities to be recognised:


Circle: When x and y are both squared and their coefficients are the same including the sign the result is a circle.


Parabola: When either x or y is squared, but not both, the result is a parabola.


Ellipse: When both x and y are squared and the coefficients are positive but different, the result is an ellipse.


Hyperbola: When x and y are both squared, and one of the coefficients is negative and the other is positive, the result is a hyperbola.

 

Question 4: How to classify conic sections?

When a conic section is in its general form, the discriminant is used to categorise it. We can utilise the discriminant b^2-4ac, to determine if the conic is a parabola, circle, ellipse, or hyperbola.


The discriminant will be B^2-4AC,if the general form of the problem is Ax^2+Bxy+Cy^2+Dx+Ey+F=0, where B=0.

 

1. B^2-4AC = 0 , A=0 or C=0

2. B^2-4AC < 0, A = C

3. B^2-4AC < 0, A≠ C

4. B^2-4AC > 0

Parabola

Circle

Ellipse 

Hyperbola

 

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