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The product of perpendiculars from the f...

The product of perpendiculars from the focii upon any tangent of the ellipse `x^2/a^2+y^2/b^2=1` is `b^2`

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To prove that the product of the perpendiculars from the foci upon any tangent of the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) is \( b^2 \), we can follow these steps: ### Step 1: Write the equation of the ellipse and the tangent line The equation of the ellipse is given by: \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \] The equation of the tangent line to the ellipse at any point can be expressed in the slope-intercept form as: ...
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