Question

Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation Determine the nature of conic equation 2𝑥2−4𝑥𝑦+5𝑦2=6.

Answer 1

General form of conic sections:

A x² + B x y + C y² + D x + E y + F = 0


Now identifying conic sections by the discriminant.

1.

If A = C then the graph is a circle

2.

If B² - 4 A C < 0 then the graph is an ellipse.

3.

If B² - 4 A C > 0 then the graph is a hyperbola.

4.

If B² - 4 A C = 0 then the graph is a parabola.


In this case;

2 x² - 4 x y + 5 y² = 6

Subtract 6 to both sides:

2 x² - 4 x y + 5 y² - 6 = 0

In equation:

A x² + B x y + C y² + D x + E y + F = 0

coefficients are:

A = 2 , B = - 4 , C = 5 , D = 0 , E = 0 , F = 6


B² - 4 A C = ( - 4 )² - 4 ∙ 2 ∙ 5 = 16 - 40 = - 24 < 0

The graph is an ellipse.