The equation of the tangent to the hyperbola `16x^(2)-9y^(2)=144` at `(5,8//3)`, is

Options

A. `10x+3y=18`
B. `10x-3y=18`
C. `10x-3y=9`
D. `10x+3y=9`

Explanation

To find the equation of the tangent to the hyperbola \(16x^2 - 9y^2 = 144\) at the point \((5, \frac{8}{3})\), we can follow these steps:

### Step 1: Convert the hyperbola equation to standard form
The given equation of the hyperbola is:
\[ 16x^2 - 9y^2 = 144 \]
To convert this to standard form, we divide each term by 144:
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