Question

and identify the graph of the parametric curve. in exercises 11–26, use an algebraic method to eliminate the parameter 19. ( x = 4 - t^2, y = t ) hint: eliminate ( t ) and solve for ( x ) in terms of ( y ).

Explanation:

Step1: Substitute \( t \) with \( y \)

Given \( y = t \), we can substitute \( t \) in the equation for \( x \).
The equation for \( x \) is \( x = 4 - t^2 \). Substituting \( t = y \), we get \( x = 4 - y^2 \).

Step2: Rearrange the equation (optional, for standard form)

We can rewrite \( x = 4 - y^2 \) as \( y^2 = 4 - x \), which is the standard form of a parabola that opens to the left.

Answer:

The equation after eliminating the parameter is \( x = 4 - y^2 \) (or \( y^2 = 4 - x \)), and the graph is a parabola opening to the left.