Identifying Conic Sections

Linear equations

Trigonometry

Conic sections

Quadratic equations

ax^2 + bx + c = 0

ax^2 + bxy + cy^2 + dx + ey + f = 0

ax + by + c = 0

ax^2 + by^2 = c

Coefficients of x^2 and y^2 have different signs

Coefficient of x^2 is zero

Coefficient of x^2 equals coefficient of y^2

Coefficient of y^2 is zero

Parabola

Ellipse

Circle

Hyperbola

Coefficients of x^2 and y^2 are equal

Coefficients of x^2 and y^2 have different signs

Only one of x^2 or y^2 terms is present

Both x^2 and y^2 terms are present

Ellipse

Parabola

Circle

Hyperbola

Coefficients of x^2 and y^2 have different signs

Only one of x^2 or y^2 terms is present

Coefficients of x^2 and y^2 are equal

Coefficients of x^2 and y^2 are not equal but have the same sign

Different signs for coefficients of x^2 and y^2

Only one squared term present

Equal coefficients for x^2 and y^2

Same sign but different coefficients for x^2 and y^2

Only one of x^2 or y^2 terms is present

Coefficients of x^2 and y^2 are not equal and have different signs

Coefficients of x^2 and y^2 are equal

Coefficients of x^2 and y^2 have the same sign

Equal coefficients for x^2 and y^2

Same sign for coefficients of x^2 and y^2

Different signs for coefficients of x^2 and y^2

Only one squared term present