Hyperbola: **When x and y are both squared, and exactly one of the coefficients is negative and exactly one of the coefficients is positive**. The equation 4y^{2} – 10y – 3x^{2} = 12 is an example of a hyperbola.

The section of the conic section is **the curve which is obtained as the intersection of the cone surface with the plane**; the three types are: eclipse, parabola, and hyperbolas. The conic section can be drawn on the coordinate plane.

If the distance of the focus from the center of the hyperbola is 'c' and the distance of the vertex of the hyperbola from the center is 'a', then eccentricity of hyperbola **e = c/a**. Another formula to find the eccentricity of hyperbola is e=√1−b2a2 e = 1 − b 2 a 2 .

**The major axis is the longest diameter of the ellipse** (usually denoted by 'a'), going through the center from one end to the other, at the broad part of the ellipse. Whereas the minor axis is the shortest diameter of ellipse (denoted by 'b'), crossing through the center at the narrowest part.

The equation of an ellipse written in the form **(x−h)2a2+(y−k)2b2=1**. The center is (h,k) and the larger of a and b is the major radius and the smaller is the minor radius.

If the intersection point is double, the line is a tangent line. Intersecting with the line at infinity, each conic section has two points at infinity. **If these points are real, the curve is a hyperbola; if they are imaginary conjugates, it is an ellipse; if there is only one double point, it is a parabola**.

Calculating the Value of Eccentricity (Eccentricity Formula):

Eccentricity of Circle: | For a Circle, the value of Eccentricity is equal to 0. |
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Eccentricity of Parabola: | For a Parabola, the value of Eccentricity is 1. |

The Eccentricity of Hyperbola: | For a Hyperbola, the value of Eccentricity is: √a2+b2a |

Hyperbola: **When x and y are both squared, and exactly one of the coefficients is negative and exactly one of the coefficients is positive**. The equation 4y^{2} – 10y – 3x^{2} = 12 is an example of a hyperbola.

The general equation of an ellipse is written as: x 2 a 2 + y 2 b 2 = 1. and the eccentricity formula is written as. **1 − b 2 a 2**. For an ellipse, a and b are the lengths of the semi-major and semi-minor axes respectively.

The only difference between the circle and the ellipse is that **in an ellipse, there are two radius measures, one horizontally along the x-axis, the other vertically along the y-axis**. Clearly, for a circle both these have the same value. By convention, the y radius is usually called b and the x radius is called a.

The foci of the ellipse are **the two reference points that help in drawing the ellipse**. The foci of the ellipse lie on the major axis of the ellipse and are equidistant from the origin. An ellipse represents the locus of a point, the sum of the whose distance from the two fixed points are a constant value.

The equation of a hyperbola written in the form **(x−h)2a2−(y−k)2b2=1**. The center is (h,k), a defines the transverse axis, and b defines the conjugate axis.

When an ellipse is not centered at the origin, we can still use the standard forms to find the key features of the graph. When the ellipse is centered at some point, (h,k),we use the standard forms (x−h)2a2+(y−k)2b2=1, a>b for horizontal ellipses and (x−h)2b2+(y−k)2a2=1, a>b for vertical ellipses.

**RHO value of parabola is 0.5, RHO value of Ellipse is between 0&0.5,RHO value of hyperbola is between 0.5&1**.

Formula for the focus of an Ellipse

The formula generally associated with the focus of an ellipse is **c2=a2−b2** where c is the distance from the focus to center, a is the distance from the center to a vetex and b is the distance from the center to a co-vetex .

Arithmetic questions **enable you to assess users' knowledge and comprehension of mathematics and number theory**. You can ensure each respondent receives a unique question by including variables enclosed with curly braces that randomly generate numbers within the problem.

Eligibility Criteria for Bank PO exam

Age of the applicant | 20 years to 30 years* |
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Nationality of the applicant | Indian** |

Educational qualification of the applicant | Should have a graduation degree from a recognised university |

What are called routers? Explanation: **The network interconnection devices that operate at the network layer** are usually called routes, which at this point should hopefully come as no surprise to you.

Physical World

1 DC motor as generator. **Brushed DC motors can be used as DC generators**. The underlying physical principle is the law of induction. Rotating the motor shaft moves the winding segment through the sinusoidal varying magnetic flux in the air gap.

**Indian History can be classified into three periods:**

- Ancient India.
- Medieval India.
- Modern India.

Dated : 29-May-2022

Category : Education