The number of real tangents that can be drawn | vedclass

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(C) The equation of the ellipse is $3x^2 + 5y^2 = 32$,which can be written as $\frac{x^2}{32/3} + \frac{y^2}{32/5} = 1$.To determine the position of t

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(C) The equation of the ellipse is $3x^2 + 5y^2 = 32$,which can be written as $\frac{x^2}{32/3} + \frac{y^2}{32/5} = 1$.To determine the position of the point $(3, 5)$ with respect to the ellipse,we evaluate the expression $S = 3x^2 + 5y^2 - 32$ at $(3, 5)$.$S = 3(3)^2 + 5(5)^2 - 32 = 3(9) + 5(25) - 32 = 27 + 125 - 32 = 120$.Since $S > 0$,the point $(3, 5)$ lies outside the ellipse.For any point lying outside an ellipse,exactly two real tangents can be drawn to the ellipse.

The number of real tangents that can be drawn to the ellipse $3x^2 + 5y^2 = 32$ passing through $(3, 5)$ is

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