Find the eccentricity of the ellipse 3x2 + 4y2 = 12 and the equation of the tangent to the ellipse at the point (1, 3/2). If this tangent meets the y-axis at the point G, and S and S′ are the foci of the ellipse, find the area of triangle SS′G.
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Expert's answer
2021-08-17T10:36:02-0400
3x2+4y2=12
Differentiate both sides with respect to x
6x+8yy′=0
y′=−4y3x
Point (1,3/2)
y′(1,23)=−4(23)3(1)=−21
The equation of the tangent in point-slope form
y−23=−21(x−1)
The equation of the tangent in slope-intercept form
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