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Answer the following: Find the equation of the tangent to the ellipse x2 + 4y2 = 100 at (8, 3)

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Question

Answer the following:

Find the equation of the tangent to the ellipse x2 + 4y2 = 100 at (8, 3)

Sum
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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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Chapter 7: Conic Sections - Miscellaneous Exercise 7 [Page 178]

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