The angle between pair of tangents to the curve `7x^(2)-12y^(2)=84` from the point `M(1,2)` is

Options

A. `2tan^(-1)"(1)/(2)`
B. `2tan^(-1)2`
C. `2(tan^(-1).(1)/(3)+tan^(-1).(1)/(2))`
D. `2tan^(-1)3`

Explanation

To find the angle between the pair of tangents to the hyperbola given by the equation \(7x^2 - 12y^2 = 84\) from the point \(M(1,2)\), we can follow these steps:

### Step 1: Rewrite the equation of the hyperbola
The given equation of the hyperbola is:
\[ 7x^2 - 12y^2 = 84 \]
We can rewrite it in standard form by dividing through by 84:
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