# 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.

#### 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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