Find the equations of the tangent and normal to the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ at the point $\left(x, y_{0}\right)$.

Answer

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Video Transcript

The question says we have to find the question of tangent and normal to the parabola by square equals to four X at the point a T square comma two way T. So now moving towards the solution and for the question by square equals to four X. The slope of the tangent at point X. Common way will be D Y by dx into by square. It was too foreign to way. Day by dx affects So to y into day. Bye Bye. will be equal to 40. So from here divided by D X will be equal to four by two Y. That is two way. Bye bye. Now, slope of the tangent at point a T square comma 2 80 Will be equal to two into a by 280 equals to one by T. So slope of the normal will be minus T. Now, the question of that engine at 0.80 square comma 2 80 will be By -2 80 equals to one by T into X -80 square. So It will be zero. Sorry, TY -280 sq minus equals two x minus 80 square now moving further. So, And the question of the normal at the 0.80 sq comma to 80 will be by minus 2 80 equals two minus T into x minus 80 square. So which implies that t x plus Y will be called to two eyes of 80 Plus 80 square. And so this will be the answer to the question. Thank you.

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