Intercepting the Tangent

Geometry Level 2

A tangent to the ellipse x 2 4 + y 2 = 1 \dfrac{x^2}{4} + y^2 = 1 , is drawn such that the point of tangency is in the first quadrant and the tangent has a slope of 1 3 \dfrac{-1}{\sqrt{3}} . What is the y-intercept of this tangent line ?


The answer is 1.5275.

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