Question

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

Answer 1

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]}