Prove-that-for-all-values-of-u-the-point-a-cosh-u-b-sinh-u-lies-on-the-hyperbola-whose-equation-is-x-2-a-2-y-2-b-2-1-And-that-the-tangent-at-that-point-is-x-a-cosh-u-

FacebookTweetPin

Question Number 28468 by tawa tawa last updated on 26/Jan/18

$$\mathrm{Prove}\mathrm{that}\mathrm{for}\mathrm{all}\mathrm{values}\mathrm{of}\mathrm{u},\mathrm{the}\mathrm{point}[\mathrm{a}\cosh \left(\mathrm{u}\right),\mathrm{b}\sinh \left(\mathrm{u}\right)]\mathrm{lies}\mathrm{on}\mathrm{the}$$$$\mathrm{hyperbola}\mathrm{whose}\mathrm{equation}\mathrm{is}.\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}-\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$$$$\mathrm{And}\mathrm{that}\mathrm{the}\mathrm{tangent}\mathrm{at}\mathrm{that}\mathrm{point}\mathrm{is}:\frac{\mathrm{x}}{\mathrm{a}}\cosh \left(\mathrm{u}\right)-\frac{\mathrm{y}}{\mathrm{b}}\sinh \left(\mathrm{u}\right)$$

Terms of Service
Privacy Policy
Contact: info@tinkutara.com

FacebookTweetPin