Which of the following represents the equation of
−
2
x
2
+
8
x
y
+
1
=
0
\displaystyle -{2}{x}^{{2}}+{8}{x}{y}+{1}={0}
−
2
x
2
+
8
x
y
+
1
=
0
when rotated through
θ
=
45
∘
\displaystyle \theta={45}^{\circ}
θ
=
45
∘
?
3
(
x
′
)
2
+
2
x
′
y
′
−
5
(
y
′
)
2
+
1
=
0
\displaystyle {3}{\left({x}'\right)}^{{2}}+{2}{x}'{y}'-{5}{\left({y}'\right)}^{{2}}+{1}={0}
3
(
x
′
)
2
+
2
x
′
y
′
−
5
(
y
′
)
2
+
1
=
0
3
(
x
′
)
2
+
2
x
′
y
′
+
5
(
y
′
)
2
+
1
=
0
\displaystyle {3}{\left({x}'\right)}^{{2}}+{2}{x}'{y}'+{5}{\left({y}'\right)}^{{2}}+{1}={0}
3
(
x
′
)
2
+
2
x
′
y
′
+
5
(
y
′
)
2
+
1
=
0
3
(
x
′
)
2
+
2
x
′
y
′
−
5
(
y
′
)
2
−
1
=
0
\displaystyle {3}{\left({x}'\right)}^{{2}}+{2}{x}'{y}'-{5}{\left({y}'\right)}^{{2}}-{1}={0}
3
(
x
′
)
2
+
2
x
′
y
′
−
5
(
y
′
)
2
−
1
=
0
3
(
x
′
)
2
−
2
x
′
y
′
−
5
(
y
′
)
2
+
1
=
0
\displaystyle {3}{\left({x}'\right)}^{{2}}-{2}{x}'{y}'-{5}{\left({y}'\right)}^{{2}}+{1}={0}
3
(
x
′
)
2
−
2
x
′
y
′
−
5
(
y
′
)
2
+
1
=
0
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