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Question
Answer the following:
Find the equation of the tangent to the ellipse x2 + 4y2 = 100 at (8, 3)
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Solution
Given equation of ellipse is x2 + 4y2 = 100
∴ `x^2/100 + y^2/25` = 1
Comparing this equation with `x^2/"a"^2 + y^2/"b"^2` = 1, we get
a2 = 100 and b2 = 25
Equation of tangent to the ellipse
`x^2/"a"^2 + y^2/"b"^2` = 1
at (x1, y1) is `("xx"_1)/"a"^2 + (yy_1)/"b"^2` = 1
∴ Equation of tangent at (8, 3) is
`(8x)/100 + (3y)/25` = 1
∴ `(2x)/25 + (3y)/25` = 1
∴ 2x + 3y = 25.
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