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How do you convert #x^2 + y^2 = 49# into parametric equations?

Answer 1

Elijah Abram

See below

There are infinite ways of do that

Given #x=f(t)# and # y=g(t)# such that

#f^2(t)+g^2(t) equiv 49# are feasible parameterizations.

Ex.

#f(t) =(7 t)/sqrt(1+t^2)# #g(t) =7/sqrt(1+t^2)#

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Answer 2

Evelyn Agard

To convert the equation (x^2 + y^2 = 49) into parametric equations, we can use the trigonometric parameterization. Let (x = 7\cos(t)) and (y = 7\sin(t)), where (t) is a parameter ranging from (0) to (2\pi).

Substituting these expressions into the equation (x^2 + y^2 = 49), we get:

[(7\cos(t))^2 + (7\sin(t))^2 = 49] [49\cos^2(t) + 49\sin^2(t) = 49] [49(\cos^2(t) + \sin^2(t)) = 49] [49 = 49]

This is true for all values of (t) from (0) to (2\pi). Hence, the parametric equations for the circle (x^2 + y^2 = 49) are:

[x = 7\cos(t)] [y = 7\sin(t)]

Where (t) ranges from (0) to (2\pi).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.