Identifying A=1, B=-1, and C=-3, we compute B^2-4 A C=13>0 . The equation is hyperbolic.

Name: Problem 20, Chapter 13: Advanced Engineering Mathematics
Uploaded: 2021-10-27T20:38:54-08:00
Duration: 3 min 47 s
Channel: Charles Machakwa
Description: Identifying A=1, B=-1, and C=-3, we compute B^2-4 A C=13>0 . The equation is hyperbolic.

step 1 Here we're given that the hyperbolic sign of x is equal to 3 over 2 and we are to find the rest

Identifying A=1, B=-1, and C=-3, we compute B^2-4 A C=13>0 ....

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Key Concepts

Hyperbola

A hyperbola is a type of conic section characterized by a discriminant value greater than zero (B² - 4AC > 0). It consists of two separate branches that mirror each other, and its geometric and algebraic properties distinguish it from other conic sections. The condition coming from the discriminant ensures that the quadratic equation represents a hyperbola.

Conic Sections

Conic sections are curves obtained by intersecting a plane with a double-napped cone. They include ellipses, parabolas, and hyperbolas, each with distinct properties based on the angle of intersection between the plane and the cone. Their general quadratic equations allow classification by evaluating the coefficients of the squared terms.

Discriminant in Conic Sections

The discriminant in the context of conic sections, given by B² - 4AC from the general quadratic equation Ax² + Bxy + Cy² + Dx + Ey + F = 0, is a key tool for determining the type of conic. Its value indicates whether the conic is an ellipse (or circle), parabola, or hyperbola, by measuring the relationship between the quadratic coefficients.

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