Question

How do you graph `\frac { ( x + 1) ^ { 2} } { 49} + \frac { ( y - 2) ^ { 2} } { 36} = 1`?

Answer 1

Please see below.

Explanation:

This is an equation of an ellipse as it is of the form `(x-h)^2/a^2+(y-k)^2/b^2=1`,

In such equations, `(h,k)` is the center of the ellipse and the two axes are `2a` and `2b`, along `x`-axis and `y`-axis respectively. The larger being major axis and smaller one being minor axis.

Hence in `(x+1)^2/49+(y-2)^2/36=1`,

center is `(-1,2)`

Major axis is `2xx7=14` and minor axis is `2xx6=12`.

Vertex (at the ends of major axis are given by `(-1+-7,2)` i.e. `(-8,2)` and `(6,2)`

and co-vertex (at the ends of minor axis are given by `(-1,2+-6)` i.e. `(-1,8)` and `(-1,-4)`.

The graph looks like as follows.

graph{(x+1)^2/49+(y-2)^2/36=1 [-16, 14, -5.5, 9.5]}