Find the locus of the-mid points of the chords of the circle `x^2 + y^2=16`, which are tangent to the hyperbola `9x^2-16y^2= 144`
Text Solution
AI Generated Solution
To find the locus of the midpoints of the chords of the circle \(x^2 + y^2 = 16\) that are tangent to the hyperbola \(9x^2 - 16y^2 = 144\), we can follow these steps:
### Step 1: Rewrite the equations
First, let's rewrite the equation of the hyperbola in standard form. We divide the entire equation by 144:
\[
\frac{9x^2}{144} - \frac{16y^2}{144} = 1
\]
...
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