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= (x+1)/(4)`

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


`y=2( (x+1)/(4) )^(2)+3( (x+1)/(4) )-4 \\ \\ y=2( ( x^(2) +2x+1)/(16) )+ (3(x+1))/(4) -4 \\ \\ y= ( x^(2) +2x+1)/(8)+ (3(x+1))/(4)-4 \\ \\ y= ( x^(2) +2x+1+6x+6-32)/(8) \\ \\ y= ( 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