Tangents are drawn from any point on the hyperbola `(x^2)/9-(y^2)/4=1` to the circle `x^2+y^2=9` . Find the locus of the midpoint of the chord of contact.

Explanation

To find the locus of the midpoint of the chord of contact from a point on the hyperbola \( \frac{x^2}{9} - \frac{y^2}{4} = 1 \) to the circle \( x^2 + y^2 = 9 \), we can follow these steps:

### Step 1: Identify a point on the hyperbola
Let the point on the hyperbola be given in parametric form:
\[ P(3 \sec \theta, 2 \tan \theta) \]
This is derived from the hyperbola's equation where \( a^2 = 9 \) and \( b^2 = 4 \).
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