The angle between the tangents drawn from the | vedclass

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Question

(A) Given the hyperbola equation: $16x^2 - 25y^2 = 400$. Dividing by $400$,we get: $\frac{x^2}{25} - \frac{y^2}{16} = 1$. Here,$a^2 = 25$ and $b^2 = 1

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$\pi /2$

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(A) Given the hyperbola equation: $16x^2 - 25y^2 = 400$. Dividing by $400$,we get: $\frac{x^2}{25} - \frac{y^2}{16} = 1$. Here,$a^2 = 25$ and $b^2 = 16$. The director circle of a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ is given by $x^2 + y^2 = a^2 - b^2$. Substituting the values,the director circle is $x^2 + y^2 = 25 - 16 = 9$. Now,check if the point $(2\sqrt{2}, 1)$ lies on this circle: $(2\sqrt{2})^2 + (1)^2 = 8 + 1 = 9$. Since the point $(2\sqrt{2}, 1)$ lies on the director circle,the tangents drawn from this point to the hyperbola are perpendicular to each other. Therefore,the angle between the tangents is $\pi /2$.

The angle between the tangents drawn from the point $(2\sqrt{2}, 1)$ to the hyperbola $16x^2 - 25y^2 = 400$ is ........

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