Transform the given parametric equations into rectangular form. Then identify the conic. x= 5cos(t) y= 2sin(t)

Solution : Option D

Step-by-step explanation:

The first thing we want to do here is isolate the cos(t) and sin(t) for both the equations --- ( 1 )

x = 5cos(t) ⇒ x / 5 = cos(t)

y = 2sin(t) ⇒ y / 2 = sin(t)

Let's square both equations now. Remember that cos²t + sin²t = 1. Therefore, we can now add both equations after squaring them --- ( 2 )

( x / 5 )² = cos²(t)

+ ( y / 2 )² = sin²(t)

x² / 25 + y² / 4 = 1

Remember that addition indicates that the conic will be an ellipse. Therefore your solution is option d.

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).

130.66 for edgedunity students