How do you graph # (x - 2)^2 + 3(y - 2)^2 = 25#?

1 Answer
Jul 22, 2017

Answer:

Please see below.

Explanation:

#(x-2)^2+3(y-2)^2=25# is the equation of an ellipse, as can be seen from the following

#(x-2)^2+3(y-2)^2=25#

#=>(x-2)^2/25+3(y-2)^2/25=1#

or #(x-2)^2/5^2+(y-2)^2/(5/sqrt3)^2=1#

an ellipse, whose center is #(2,2)# and major axis is #2xx5=10# parallel to #x#-axis and minor axis is #2xx5/sqrt3=10/sqrt3# parallel to #x#-axis.

End points of major axis are #(2+-5,2)# i.e. #(7,2)# and #(-3,2)#

End points of minor axis are #(2,2+-5/sqrt3)# i.e. #(2,2-5/sqrt3)# and #(2,2+5/sqrt3)#

It appears as follows:

graph{((x-2)^2+3(y-2)^2-25)((x+3)^2+(y-2)^2-0.02)((x-7)^2+(y-2)^2-0.02)((x-2)^2+(y-2+5/sqrt3)^2-0.02)((x-2)^2+(y-2-5/sqrt3)^2-0.02)=0 [-8.5, 11.5, -3.2, 6.8]}