The angle between the tangents drawn from a p | vedclass

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(D) The equation of the ellipse 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 poi

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$90^{\circ}$

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(D) The equation of the ellipse 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 point $P(-3, 2)$ lies on the ellipse because $4(-3)^2 + 9(2)^2 = 4(9) + 9(4) = 36 + 36 = 72 
eq 36$. Wait,let us recheck: $4(9) + 9(4) = 36 + 36 = 72$. The point $(-3, 2)$ is actually outside the ellipse.The director circle of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is $x^2 + y^2 = a^2 + b^2$.Here,$x^2 + y^2 = 9 + 4 = 13$.Check if the point $(-3, 2)$ lies on the director circle: $(-3)^2 + (2)^2 = 9 + 4 = 13$.Since the point $(-3, 2)$ lies on the director circle,the angle between the tangents drawn from this point to the ellipse is $90^{\circ}$.

The angle between the tangents drawn from a point $(-3, 2)$ to the ellipse $4x^2 + 9y^2 - 36 = 0$ is

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