# How do you identity if the equation #x^2+y^2-20x+30y-75=0# is a parabola, circle, ellipse, or hyperbola and how do you graph it?

##### 2 Answers

Set your compass for a radius of 20 units, place the center at

#### Explanation:

Here is a reference Conic section - General Cartesian form that tells how to identitfy any equation of the form:

In the given equation,

where,

Add

Add 75 to both sides of the equation:

Set the middle term in the right side of the pattern,

Solve for h:

This allows us to substitute

Set the middle term in the right side of the pattern,

Solve for h:

This allows us to substitute

Combine the constants on the right:

Express the constant as a square:

This is the equation of a circle with a center

**It is the equation of circle.**

#### Explanation:

As the coefficients of

**It is the equation of circle.**

and it can be written as

Hence this is an equation of a circle with center as

graph{x^2+y^2-20x+30y-75=0 [-31.17, 48.83, -34.88, 5.12]}

Also check here

As