Question

Answer the following:

Find the equation of the tangent to the hyperbola 7x² − 3y² = 51 at (−3, −2)

Answer 1

The equation of the hyperbola is 7x² − 3y² = 51

i.e. `x^2/((51/7)) - y^2/17` = 1

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

a² = `51/7`, b² = 17

The equation of the tangent to `x^2/"a"^2 - y^2/"b"^2` = 1 at the point (x₁, y₁) on it is

`("xx"_1)/"a"^2 = (yy_1)/"b"^2` = 1

∴ the equation of the tangent to the given hyperbola at the point (–3, –2) is

`(-3x)/((51/7)) + (2y)/17` = 1

∴ `(-7x)/17 + (2y)/17` = 1

∴ 7x – 2y + 17 = 0.