Question

in exercises 61–64, solve the problem without using a calculator. 61. multiple choice which of the following points corresponds to ( t = -1 ) in the parametrization ( x = t^2 - 4 ), ( y = t + \frac{1}{t} )? (a) ( (-3, -2) ) (b) ( (-3, 0) ) (c) ( (-5, -2) ) (d) ( (-5, 0) ) (e) ( (3, 2) )

Explanation:

Step1: Calculate x when t = -1

Substitute \( t = -1 \) into the equation for \( x \): \( x = t^2 - 4 \).
\( x = (-1)^2 - 4 = 1 - 4 = -3 \)

Step2: Calculate y when t = -1

Substitute \( t = -1 \) into the equation for \( y \): \( y = t + \frac{1}{t} \).
\( y = -1 + \frac{1}{-1} = -1 - 1 = -2 \)

Answer:

A. \((-3, -2)\)