Sketch the ellipse #(x+1)^2 +4(y-3)^2-1=0#. Indicate the coordinates of the centre and the endpoints of the minor and major axes?

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Answer 1 · 2017-07-06T15:16:46

Coordinates of center are #(-1,3)#; endpoints of major axis are #(-2,3)# and #(0,3)# and that of minor axis are #(-1,2.5)# and #(-1,3.5)#.

Let us write the given equation in general form of equation of ellipse

#(x-h)^2/a^2+(y-k)^2/b^2=1#, where #(h,k)# is the center of ellipse and major axis is #2a# and minor axis is #2b# (if #a>b#).

The equation #(x+1)^2+4(y-3)^2-1=0# can be written as

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

Hence, coordinates of center are #(-1,3)# and major axis is #2# and minor axis is #1#.

As endpoints of major axis would be #a=1# units on either side of the center parallel to #x#-axis,

end points of major axis are #(-2,3)# and #(0,3)#

similarly endpoints of minor axis would be #a=1/2# units on either side of the center parallel to #y#-axis,

end points of minor axis are #(-1,2.5)# and #(-1,3.5)#

graph{(x+1)^2+4(y-3)^2-1=0 [-3.385, 1.615, 1.25, 3.75]}