# list the intercepts and test for symmetry x^2+49y^2=49 List the intercepts or are there no intercepts

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List the intercepts and test for symmetry `x^2+49y^2=49`

(1) If x=0 `49y^2=49==>y^2=1==>y=+-1`

**The y-intercepts are 1 and -1**

(2) If y=0 `x^2=49==>x=+-7`

**The x-intercepts are 7 and -7**

(3) If we substitute (-x) for x we get `(-x)^2+49y^2=49 ==> x^2+49y^2=49` so **the graph is symmetric across the y-axis**

If we substitute (-y) for y we get `x^2+49(-y)^2=49==>x^2+49y^2=49` so **the graph is symmetric across the x-axis.**

Replacing x with (-x) and y with (-y) does not change the relation,

**so the graph is symmetric about the origin.**

This is not a surprise as `x^2+49y^2=49==>x^2/49+y^2/1=1`

This is an ellipse centered at the origin.

**Sources:**