Question #f1260

1 Answer
Alexander L.
Dec 2, 2015

#y=+-5/4(16-x^2)^0.5#

Explanation:

#x=4costheta# & #y=5sintheta#
Square both sides
#x^2=16cos^2theta# & #y^2=25sin^2theta#
Notice that #sin^2theta=1-cos^2theta#
#y^2=25(1-cos^2theta)-># Equation 1

Substitute #cos^2theta=x^2/16# into Equation 1.

#y^2=25(1-x^2/16)#
Rearrange this to get:
#y=+-5/4(16-x^2)^0.5#

From your domain #-pi/2<=theta<=pi/2#

We find that x ranges from #{x;0<=x,+4}#
and y ranges from #{y;-5<=y<=5}#.
The fact that #x=4costheta# & #y=5sintheta# takes the form of a parametric curve (oval shape), we can draw an oval that is restricted by the given conditions.
graph{5/4(16-x^2)^0.5 [0, 4, -5, 5.5]}
The graph also reflects on the x-axis.
graph{-5/4(16-x^2)^0.5 [0, 4, -5, 5.5]}
Put the 2 graphs together.

The arrow should be pointing clockwise.

Related questions
Impact of this question
2876 views around the world
You can reuse this answer
Creative Commons License