The parabola $y=x^2$ has a vertical axis. I will certainly construe your $23.5^circ$ to suppose $23.5^circ$ from the vertical.
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Draw the $x$-axis pointing to the appropriate and also the $y$-axis pointing upward.
Then draw a $u$-axis pointing in a direction $23.5^circ$ clockwise from the $x$-axis and also a $v$-axis $23.5^circ$ clockwise from the $y$-axis.
You require the equation of your rotated parabola to be $v=u^2.$
We will certainly require this:$$ ag 1eginalignu & = (cos23.5^circ)x-(sin23.5^circ) y \v & = (sin23.5^circ)x +(cos23.5^circ) yendalign$$
So $v=u^2$ becomes$$(sin23.5^circ)x +(cos23.5^circ) y = Big( (cos23.5^circ)x-(sin23.5^circ) y Big)^2.$$
For now I"ve left the derivation of $(1)$ as an exercise, but if crucial you have the right to ask around that as well.
answered May 5 "18 at 19:44
Michael HardyMichael Hardy
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If your parabola is given by:
$$ -xsin a+ycos a =left( xcos a+ysin a-h ight)^2+k $$
transforming $h$ will certainly move it along $x$ axis, transforming $k$ will relocate it along the $y$ axis. Altering $a$ will tilt it.
See demo: https://www.desmos.com/calculator/hguanwbkbu
answered May 5 "18 at 19:08
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