Quadratic curve is a curve drawn to get a given quadratic equation. The equation on the form y=$ax^2+bx+c$ is named as quadratic equation. The y value depends upon a, b, c, and x. For a given equation a, b and c will probably be constant, so on-line of y adjustments for different ideals of x. You can plot it in a graph result within quadratic curve.

The shape of the curve can be determined from the discriminant: $B^2 - 4AC$.

## Formula

The general equation of degree 2 in two variables x and y can be written as:

$ax^{2} + bxy + cy^{2}$ + $dx$ + $ey$ = $f$

where a b c d are the fixed coefficients of the equation and f is the constant term.
Here at least one of a, b, c not equal to zero, and an equation setting this function equal to zero gives rise to a conic section.

## Steps

Below you could see the steps to identify types of curve:
Step 1: Expand the given equation and simplify it.

Step 2: Rearrange the given equation in standard form. Ax$^{2}$ + Bxy + Cy$^{2}$ + Dx + Ey + F = 0

Step 3: Compare the equation with the standard form to find A, B, C ,D ,E and F.

Step 4: Find $B^{2}- 4AC$ check

If it is equal to 0 then it is a parabola

Less than zero it is known to be ellipse or

Greater than zero it is known to be a hyperbola.

## Examples

Some of the examples based on quadratic curve are given below.

Example 1: Identify the type of curve for the equation

$15x^{2} - 30x + 25y^{2} - 300y$ = 20

Solution:
Given expression is 15x$^{2}$ - 30x + 25y$^{2}$ - 300y = 20  ................ 1

Standard form: $Ax^{2} + Bxy + Cy^{2} + Dx + Ey + F$ = 0

After rearranging the given expression in standard form we get,

$15x^{2} + 0xy + 25y^{2} - 30x -300y -20$ = 0  .......................... 2

Comparing equation 1 and equation 2 we get,

A = 15
B = 0
C = 25

$B^{2}$ - 4AC = 0

= 0 + 4 * 15 * 25

= 1500

Therefore the given equation represents a hyperbola

Example 2: Identify the type of curve for the equation

$x^{2} - 2y - 4x + 22$ = 0

Solution:

Given expression is $x^{2} - 2y - 4x + 22$ = 0  ................ 1

Standard  form: $Ax^{2} + Bxy + Cy^{2} + Dx + Ey + F$ = 0

After rearranging the given expression in standard form we get,

$0x^{2} + 0xy + x^{2} - 4x - 2y + 22$ = 0  ............ 2

Comparing the above two equations we get

A = 0

B = 0

C = 1

$B^{2} - 4AC$

= $0^{2}$ - 4 * 0 * 1

= 0
Therefore the given equation represents a parabola

Example 3: Identify the type of curve for the equation

$14x^{2}$ - 16x + 10y^{2} - 100y$= - 10 Solution: Given expression is$14x^{2} - 16x + 10y^{2} - 100y$= - 10 ...................... 1 Standard form:$Ax^{2} + Bxy + Cy^{2} + Dx + Ey + F$= 0 After rearranging the given expression in standard form we get,$14x^{2} + 0xy + 10y^{2} - 16x - 100y + 10$= 0 ............................. 2 Comparing two equations we get A = 14 B = 0 C = 10$B^{2} - 4AC$=$0^{2}\$ - 4 * 14 * 10

= -560
Therefore the given curve is either an ellipse or a circle