Question

How do you sketch `4x ^ { 2} + y ^ { 2} - 8x - 4y - 28= 0`?

Answer 1

Please see below.

Explanation:

`4x^2+y^2-8x-4y-28=0` is the equation of an ellipse, as can be seen from the following

`4x^2+y^2-8x-4y-28=0`

`hArr4(x^2-2x+1)-4+(y^2-4y+4)-4-28=0`

or `4(x-1)^2+(y-2)^2=36`

or `(x-1)^2/9+(y-2)^2/36=1` or `(x-1)^2/3^2+(y-2)^2/6^2=1`

an ellipse, whose center is `(1,2)` and major axis is `2xx6=12` parallel to `y`-axis and minor axis is `2xx3=6` parallel to `x`-axis.

End points of major axis are `(1,2+-6)` i.e. `(1,-4)` and `(1,8)`

End points of minor axis are `(1+-3,2)` i.e. `(-2,2)` and `(4,2)`

It appears as follows:

graph{(4x^2+y^2-8x-4y-28)((x-1)^2+(y-2)^2-0.06)((x-1)^2+(y+4)^2-0.06)((x-1)^2+(y-8)^2-0.06)((x+2)^2+(y-2)^2-0.06)((x-4)^2+(y-2)^2-0.06)=0 [-19.5, 20.5, -8.32, 11.68]}