What is general equation of 2nd degree?

What is general equation of 2nd degree?

ax2 + 2hxy + by2 + 2gx + 2fy + C = 0, where a, h, b, g, f and c are constants. Therefore, the general second degree equation in x and y represents a circle if coefficient of x2 (i.e., a) = coefficient of y2 (i.e., b) and coefficient of xy (i.e., h) = 0.

What is the condition that the general equation of second degree should represent a pair of straight lines?

Equations of second degree will represent a pair of straight lines only if the left hand side can be resolved into two linear factors. Consider an equation y2 – 3xy + 2×2 = 0. This equation is equivalent to (y – x) (y – 2x) = 0.

What is a second degree variable?

Second-degree equations involve at least one variable that is squared, or raised to a power of two. One of the most well-known second-degree equations is the quadratic where a, b, and c are constants and a is not equal 0.

For what condition is the general equation of second degree to represent a cone?

Conditions on general second degree equation to represent a conic. Case 1: When Δ=0, the equation represents the Degenerate conics. Case 2: When Δ=0, the equation represents the Non−degenerate conics.

What is homogenous equation of second degree prove that the homogenous equation of second degree represent a pair or straight line through the origin?

The homogeneous equation of second degree ax2+2hxy+by2=0, always represents a pair of straight lines through the origin. Hence, both of these equations i.e, equation (iii) and (iv) represents the line through origin.

What do you call a second degree equation which uses the relation signs?

A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign.

What is the difference between first degree equation and second degree equation?

Equations which involve unknowns raised to a power of one are known as first degree equations. Second degree equations also exist which involve at least one variable that is squared, or raised to a power of two.

How do you factor second degree equations?

With the quadratic equation in this form:

1. Step 1: Find two numbers that multiply to give ac (in other words a times c), and add to give b.
2. Step 2: Rewrite the middle with those numbers:
3. Step 3: Factor the first two and last two terms separately:

What is Delta in 2nd degree equation?

The symbol “Δ”, read as “delta”, is generally used to represent the discriminant of a second-degree polynomial equation.