Question

Find the equation of the tangent to the hyperbola: x²/16 - y²/9 = 1 at the point in a first quadrant whose ordinate is 3.

Answer 1

Given equation of the hyperbola is  x²/16 - y²/9 = 1 

Comparing this equation with \(\frac {x^2}{a^2} - \frac {y^2}{b^2} = 1\),

We get 

a² = 16 and b² = 9

Let P (x₁, 3) be the point on the hyperbola in the first quadrant at which the tangent is drawn.

Substituting x = x₁ and y = 3 in equation of hyperbola, we get

\(\frac {x_1^2}{16} - \frac {3^2}{9} = 1\)

∴ 3√2x- 4y = 12