Parametric and Polar for BC

Front

What are parametric equations?

Back

Parametric equations express the coordinates of points on a curve as functions of a variable, typically denoted as 't'. For example, x = f(t) and y = g(t).

Front

How do you find a point from parametric equations?

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To find a point from parametric equations, substitute the given value of 't' into the equations for x and y. For example, if x = 1 - 2t and y = 4t + 1, for t = 3, x = 1 - 2(3) = -5 and y = 4(3) + 1 = 13, giving the point (-5, 13).

Front

What is the rectangular form of parametric equations?

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Front

Back

This equation represents an ellipse centered at the origin with semi-major axis 4 (along the y-axis) and semi-minor axis 3 (along the x-axis).

Front

What is the Pythagorean identity in trigonometry?

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Front

How do you determine the area enclosed by a polar curve?

Back

Front

What is the area enclosed by one loop of the curve r = cos(2θ)?

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Front

What is the rectangular form of the equations x = 2t and y = t^2 + 3?

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Front

What are the characteristics of a hyperbola?

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Front

What is the relationship between parametric equations and derivatives?

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