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?

1 Answer
Jul 6, 2017

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).

Explanation:

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]}