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**Calculus Question - Tangents to an ellipse - its got me stumped!!**

## Homework Statement

A tangent line is drawn to the ellipse x^2/25 + y^2/16 = 1 so that the part intercepted by the co-ordinate axis is a minimum. Show that it has a length of 9 units.

## Homework Equations

x^2/25 + y^2/16 = 1

## The Attempt at a Solution

I have seen this question on the forums, through a quick google search, but cannot see how the user came up with the steps and eventual answer. I think you need to differentiate the equation first and this will give you the slope at the point (where the intercepted part is a minimum). From there i can only guess, something like constructing an equation for tangent, and then solving for the x and y intercepts. Substitute into pythagoras.

I have given this a shot, but to no avail. Please Help!!!!