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
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