# Let a tangent to the curve 9x2+16y2=144 intersect the coordinate axes at the points A and B . Then, the minimum length of the line segment AB is ______

## Question

## Solution 1

The given equation is of an ellipse, which can be rewritten as (x^2/4) + (y^2/16) = 1.

The equation of the tangent to the ellipse in the slope form is y = mx + sqrt(16m^2 + 4).

The x-intercept of the tangent line (point A) is -sqrt(16m^2 + 4)/m and the y-intercept (point B) is sqrt(16m^2 + 4).

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