Find the equations of the tangents and normal to the hyperbola x2a2 - y2b2 - 1 at the point x0-y0

1a^2 (2x) 1b^2 ( dydx )=0 2yb^2dydx = 2xa^2⇒ #160; dydx = xb^2ya^2 =b^2a^2 (xy) dxdy]_(x_0,y_0) =b^2a^2× ( x_0y_0 ) ...

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Byju's Answer

Standard XII

Mathematics

Equation of Tangent at a Point (x,y) in Terms of f'(x)

Find the equa...

Question

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

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Solution

$\frac{1}{a^{2}} (2 x) - \frac{1}{b^{2}} (\frac{d y}{d x}) = 0$
$\frac{2 y}{b^{2}} \frac{d y}{d x} = \frac{2 x}{a^{2}} \Rightarrow \frac{d y}{d x} = \frac{x b^{2}}{y a^{2}} = \frac{b^{2}}{a^{2}} (\frac{x}{y})$
$\frac{d x}{d y}]_{(x_{0}, y_{0})} = \frac{b^{2}}{a^{2}} \times (\frac{x_{0}}{y_{0}})$

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Find the equations of the tangents and normal to the hyperbola x2a2−y2b2=1 at the point (x_{0},y_{0})$

1a2(2x)−1b2(dydx)=02yb2dydx=2xa2⇒dydx=xb2ya2=b2a2(xy)dxdy](x0,y0)=b2a2×(x0y0)

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

$\frac{1}{a^{2}} (2 x) - \frac{1}{b^{2}} (\frac{d y}{d x}) = 0$
$\frac{2 y}{b^{2}} \frac{d y}{d x} = \frac{2 x}{a^{2}} \Rightarrow \frac{d y}{d x} = \frac{x b^{2}}{y a^{2}} = \frac{b^{2}}{a^{2}} (\frac{x}{y})$
$\frac{d x}{d y}]_{(x_{0}, y_{0})} = \frac{b^{2}}{a^{2}} \times (\frac{x_{0}}{y_{0}})$