Identity the conic section whose equation is R=1/(2-3sinx)

  hyperbola

Step-by-step explanation:

A graphing calculator shows the equation is that of a hyperbola.

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Multiplying by the denominator gives ...

  r(2 -3sin(x)) = 1

  2r -3y = 1 . . . . . . . . substituting y=r·sin(x)

  2r = 1 +3y . . . . . . . .isolating r

  4r² = 1 +6y +9y² . . squaring both sides

  4(x² +y²) = 1 +6y +9y² . . . . . substituting x²+y² = r²

  4x² -5y² -6y -1 = 0 . . . . . . . . general form equation of a hyperbola