The number of possible tangents which can be | vedclass

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(A) The given hyperbola is $4x^2 - 9y^2 = 36$,which can be written as $\frac{x^2}{9} - \frac{y^2}{4} = 1$. Here $a^2 = 9$ and $b^2 = 4$.The slope of t

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(A) The given hyperbola is $4x^2 - 9y^2 = 36$,which can be written as $\frac{x^2}{9} - \frac{y^2}{4} = 1$. Here $a^2 = 9$ and $b^2 = 4$.The slope of the line $5x + 2y - 10 = 0$ is $m_1 = -\frac{5}{2}$.The slope of the tangent perpendicular to this line is $m = -\frac{1}{m_1} = \frac{2}{5}$.The condition for a line $y = mx + c$ to be a tangent to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ is $c^2 = a^2m^2 - b^2$.Substituting the values: $c^2 = 9\left(\frac{2}{5}\right)^2 - 4 = 9\left(\frac{4}{25}\right) - 4 = \frac{36}{25} - 4 = \frac{36 - 100}{25} = -\frac{64}{25}$.Since $c^2 Thus,the number of possible tangents is $0$.

The number of possible tangents which can be drawn to the curve $4x^2 - 9y^2 = 36$,which are perpendicular to the straight line $5x + 2y - 10 = 0$ is

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