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Question 876257: Please help me answer this question. I need the answer as soon as possible. Question: Find an equation of the line containing(3,-2) and tangent to 4x^2+y^2=8. Not using the principle of derivatives. Thank you.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! This is an ellipse with its major axis on the y axis and whose center is the origin (0,0), the point of tangent to this ellipse is the point of the negative major axis.
4x^2 + y^2 = 8
divide both sides of the = by 8
x^2/2 + y^2/8 = 1
the major axis is + or - square root of 8 = + or - 2.82
so the point is (0, -2.8) the other point is (3, -2)
standard form of line is y = mx + b, where m is slope and b is y intercept
m = (-2.8 - (-2)) / 0 - 3) = -0.8 / -3 = 0.27
y = 0.27x + b
b = y - 0.27x
b = -2 - 0.27(3)
b = -2.81 and equation of the tanget line is
y = 0.27x - 2.81
note that the difference between the negative major axis point (0, -2.82) and the y intercept is the rounding of the slope value
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