# Answer the following: Find the equations of the tangents to the hyperbola 3x2 − y2 = 48 which are perpendicular to the line x + 2y − 7 = 0 - Mathematics and Statistics

Sum

Find the equations of the tangents to the hyperbola 3x2 − y2 = 48 which are perpendicular to the line x + 2y − 7 = 0

#### Solution

The equations of tangents to the hyperbola x^2/"a"^2 - y^2/"b"^2 = 1 in terms of slope m are

y = "m"x ± sqrt("a"^2"m"^2 - "b"^2)   ...(1)

The equation of the hyperbola is 3x2 – y2 = 48

i.e., x^2/16 - y^2/48 = 1

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

a2 =16, b2 = 48

Slope of x + 2y – 7 = 0 is -1/2

The required tangent is perpendicular to it

∴ its slope = m = 2

∴ by (1), the required equations of tangents are

y = 2x ± sqrt(16(4) - 48)

∴ y = 2x ± 4.

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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 7 Conic Sections
Miscellaneous Exercise 7 | Q 2.25 | Page 178