Question

Find the region enclosed by the curves x = 3y^2 and x = y^2 + 7 List the points of intersection of these curves from bottom to top in the form (x, y).

Analyzing functions
ANSWERED
asked 2021-01-23
Find the region enclosed by the curves \(\displaystyle{x}={3}{y}^{{2}}{\quad\text{and}\quad}{x}={y}^{{2}}+{7}\)
List the points of intersection of these curves from bottom to top in the form (x, y).

Answers (1)

2021-01-24
\(\displaystyle{x}={3}{y}^{{2}},{x}={y}^{{2}}+{7}\)
\(\displaystyle{3}{y}^{{2}}={y}^{{2}}+{7}\)
\(\displaystyle{2}{y}^{{2}}={7}\)
\(\displaystyle{y}^{{2}}=\frac{{7}}{{2}}\)
\(\displaystyle{y}=\pm\sqrt{{\frac{{7}}{{2}}}}\)
\(\displaystyle{y}=\sqrt{{\frac{{7}}{{2}}}}\)
\(\displaystyle{x}={3}\times\frac{{7}}{{2}}=\frac{{21}}{{2}}\)
or \(\displaystyle{y}=-\sqrt{{\frac{{7}}{{2}}}}\)
\(\displaystyle{x}=\frac{{21}}{{2}}\)
The points: \(\displaystyle{\left(\frac{{21}}{{2}},\sqrt{{\frac{{7}}{{2}}}}\right)},{\left(\frac{{21}}{{2}},-\sqrt{{\frac{{7}}{{2}}}}\right)}\).
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