The parabola
y
=
x
2
+
5
\displaystyle {y}={x}^{{2}}+{5}
y
=
x
2
+
5
has two tangents which pass through the point
(
0
,
−
3
)
\displaystyle {\left({0},-{3}\right)}
(
0
,
−
3
)
. One is tangent to the to the parabola at
(
A
,
A
2
+
5
)
\displaystyle {\left({A},{A}^{{2}}+{5}\right)}
(
A
,
A
2
+
5
)
and the other at
(
−
A
,
A
2
+
5
)
\displaystyle {\left(-{A},{A}^{{2}}+{5}\right)}
(
−
A
,
A
2
+
5
)
. Find (the positive number)
A
\displaystyle {A}
A
.
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\displaystyle
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter DNE for Does Not Exist, oo for Infinity