Find the point on the ellipse x^2/4+y^2=1,that is nearest to the origin?

1 Answer
Feb 15, 2018

graph{x^2/4+y^2=1 [-3.464, 3.465, -1.732, 1.732]}

Explanation:

the ellipse, #x^2/4+y^2=1# has its major axis on the x-axis.

so, technically, the point nearest to the origin would be the y-intercept.

so, replacing, #x=0# in the equation #x^2/4+y^2=1#,

#0^2/4+y^2=1#
#y^2=1#
#y=+-1#

the point on the ellipse x^2/4+y^2=1,that is nearest to the origin would be, #(0,1)# and #(0,-1)#

-Sahar ;)