Given: r = 4/-2-6sintheta
What type of conic does this represent?
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Circle
Ellipse
Hyperbola
Parabola
divide by -2 ant it changes to
r = -2/(1+3sinθ)
now what do you think?
To determine the type of conic represented by the equation r = 4/-2 - 6sin(theta), we need to understand the polar equation of conics.
In polar coordinates, conic sections can be represented by the equation r = f(theta), where r is the distance from the origin to a point on the curve, and theta is the angle between the positive x-axis and the line segment connecting the origin to the point.
For each type of conic, the equation can be written in a standard form:
1. Circle: r = a, where a is a constant.
2. Ellipse: r = (a * b) / sqrt((b * cos(theta))^2 + (a * sin(theta))^2), where a and b are positive constants.
3. Hyperbola: r = (a * b) / sqrt((b * cos(theta))^2 - (a * sin(theta))^2), where a and b are positive constants.
4. Parabola: r = a / (1 + cos(theta)) or r = a / (1 - cos(theta)), where a is a positive constant.
In the given equation, r = 4/-2 - 6sin(theta), the denominator consists of only the sine function. This indicates that it doesn't fit the standard forms of any of the conic sections.
Therefore, the equation r = 4/-2 - 6sin(theta) does not represent any conic section.