When a conic is written in the standard form Ax^2 + By^2 + Cx + Dy + E = 0, you

Question

When a conic is written in the standard form Ax^2 + By^2 + Cx + Dy + E = 0, you can determine the type of conic an equation represents by comparing A & B. For each of statements below, fill in the name of the conic the that would be formed. 1. If A = B (not equal to 0), then the conic is a/an __________. 2. If A or B is 0 (but not both) then the conic is a/an _______. 3. If A and B are both non-zero and have the same sign (+ or -), then the conic is a/an _______. 4. If A and B are both non-zero and have opposite signs, then the conic is a/an _________. Using the information above, determine what conic each of the following equations represents. y^2 = 4(2x + 2y) ______ 2. 4x^2 + y^2 = 8(x + y) - 4 ________ 3. x^2 + 5 = 6x + 2y^2 ________ 4. x^2 + 4x + y^2 + 6y - 12 = 0 ______

Explanation / Answer

If A & B are equal and non zero

conic is circle (1)

If one of A or B is zero

conic is parabola (2)

If A & B are non zero and have same sign

conic is ellipse (3)

If A & B are non zero & have opposite sign

conic is hyperbola (4)

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