which conic section is represented by the polar equation $r=\\frac{3}{4+2\\sin\\theta}$?\n(1 point)\n○…

which conic section is represented by the polar equation $r=\\frac{3}{4+2\\sin\\theta}$?\n(1 point)\n○ ellipse\n○ hyperbola\n○ parabola\n○ circle

which conic section is represented by the polar equation $r=\\frac{3}{4+2\\sin\\theta}$?\n(1 point)\n○ ellipse\n○ hyperbola\n○ parabola\n○ circle

Answer

Explanation:

Step1: Rewrite to standard form

Divide numerator and denominator by 4: $$r = \frac{\frac{3}{4}}{1+\frac{1}{2}\sin\theta}$$

Step2: Identify eccentricity $e$

Compare with $r=\frac{ed}{1+e\sin\theta}$, so $e=\frac{1}{2}$

Step3: Classify conic

Since $0<e<1$, the conic is an ellipse.

Answer:

ellipse