PLEASE HELP ME Thank you Identify the equation without apply

Identify the equation without applying a rotation of axes. D) circle hyperbola A) parabola Parametric equations and a value for the parameter tare given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. 20 x 6.7 oosty 8.6 sint t B) (6, 11) A) (38) D) (6, 14) parametert Find a rectangular equation for the plane curve defined by the parametric equations. Eliminate the B) y 2, -4 sxs4 Identify the conic section that the polar equation represents. Describe the location of a directrix from the focus located at the pole. 4) 4) r 1-3 cos A) ellipse: The directrixis 1 unit(s to the right of the pole at x-1. ellipse: The directrix is 1 units to the left of the pole at x --1. hyperbola: The directrix is unit(s) to the left of the pole at x -1. D) hyperbola: The directrix is 1 unit(s) to the right of the pole at x 1.

Solution

2) x = 6 +7cost ; y = 8 +6sint ; t =pi/2

x = 6 + 7cospi/2 = 6 +7*0 = 6

y = 8 +6sinpi/2 = 8+6 = 14

(x, y) = ( 6, 14) Option D

3) x = t^3 +1 ; y = t^3 - 5

Eliminate t by substitution :

x = t^3 +1

y = t^3 -5

-------- subtract

x - y = 1+5

x -y = 6 ;

y = x -6 ; -7 <=x<=9

Option C