Maharashtra State BoardHSC Science (General) 11th
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Find the equation of the tangent to the ellipse x225+y24 = 1 which are parallel to the line x + y + 1 = 0. - Mathematics and Statistics

Sum

Find the equation of the tangent to the ellipse `x^2/25 + y^2/4` = 1 which are parallel to the line x + y + 1 = 0.

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Solution

Given equation of the ellipse is `x^2/25 + y^2/4` = 1

Comparing this equation with `x^2/"a"^2 + y^2/"b"^2` = 1, we get

a2 = 25 and b2 = 4

Slope of the given line x + y + 1 = 0 is –1.

Since the given line is parallel to the required tangents, slope of the required tangents is m = –1.

Equations of tangents to the ellipse

`x^2/"a"^2 + y^2/"b"^2` = 1 having slope m are

y = `"m"x ± sqrt("a"^2"m"^2 + "b"^2)`

∴ y = `-x  ± sqrt(25(-1)^2 + 4)`

∴ y = `-x ± sqrt(29)`

∴ x + y = `± sqrt(29)`.

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