# SOLUTION: sketch the portion of graph in the first quadrant and use symmetry to complete the rest of the graph 4x^2+16y^2=16

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 Question 233394: sketch the portion of graph in the first quadrant and use symmetry to complete the rest of the graph 4x^2+16y^2=16Answer by Edwin McCravy(8912)   (Show Source): You can put this solution on YOUR website!``` It's symmetrical with respect to the x-axis because if we replace x by -x and simplify, we get the same equation we started with: It's symmetrical with respect to the y-axis also because if we replace y by -y and simplify, we get the same equation we started with: It's symmetrical with respect to the origin because if we replace x by -x and y by -y at the same time and simplify, we also get the same equation we started with: Next we find some first quadrant points. Choose Substitute in This gives and So a point in the first quadrant is (0,1) (Actually it's a point on the BORDER of the first quadrant, on the y-axis) Choose Substitute in This gives and So a point in the first quadrant is (0,), which is about (1, .9) Choose Substitute in This gives So another point in the first quadrant is (2,0) (Actually it's another point on the BORDER of the first quadrant, this time on the x-axis) Plot those three first quadrant points: Next by the symmetry, we can reflect these three points in both the x-axis and the y-axis, (like a mirror!) and we have this: Now we can sketch the curve: Edwin```