Question

A biologist determines that the path of a bee from its hive to its foraging site can be described by the parametric equations x- 4t-1 and y-22+3t-4. Which of the following equations is the curve described by these parametric equations?
y=20x-9
y=20x+16
x^2+8x-25/8
x^2+4x-37/8

Answer 1

The correct parametric equations are:

$x=4t-1 \\ \\ y=2t^{2}+3t-4$

From first equation, we can write the value of t in terms of x to be:

$t= \frac{x+1}{4}$

Using this value of t in equation of y, we get:

$y=2( \frac{x+1}{4} )^{2}+3( \frac{x+1}{4} )-4 \\ \\ y=2( \frac{ x^{2} +2x+1}{16} )+ \frac{3(x+1)}{4} -4 \\ \\ y= \frac{ x^{2} +2x+1}{8}+ \frac{3(x+1)}{4}-4 \\ \\ y= \frac{ x^{2} +2x+1+6x+6-32}{8} \\ \\ y= \frac{ x^{2} +8x-25}{8}$

Thus, the curve in option C is described by the given parametric equations.

Answer 2

1. Counter clockwise

2. (30,401)

3. t=2(x-3)

4. She should have taken both the positive and negative square root

5. y= x^2+8x-25/8

6. Hyperbola

7. (A) the ellipse is positive meaning it is above the x axis it is going counter clock wise so the arrow on top of the ellipse is pointing left and the arrow on the bottom of the ellipse is pointing right