Given a parabola \$Y=X^2,\$ how deserve to I modify the equation so the parabola tilts away from it’s vertical orientation? For instance, a solar collector might have a tilt of \$23.5\$ degrees. How would certainly this look as a polynomial?  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.

You are watching: How to tilt a parabola

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 1eginalignu & = (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.

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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

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answered May 5 "18 at 19:08 ITAITA
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