Find the equation of common tangent to 9x2 ndash 16y2 144 and x2 y2 9 ........

Mathematics (NDA) Coordinate Geometry

Find the equation of common tangent to 9x² – 16y² = 144 and x² + y² = 9?

y =±3 √2/7 x ±15/√5

y =±3 √2/7 x ±1/√7

y =± √2/7 x ±15/√7

y =±3 √2/7 x ±15/√7

Hyperbola 9x² – 16y² = 144

X²/16 -y²/9 =1

Circle x² + y² = 9

Equation of tangent y = mx +√16m² -9 hyperbola

Equation of tangent y =m^’ x +3√1+m^{’ 2}circle

For Common tangent m=m’

3√1+m^{’ 2}=√16m² -9

9(1+m^{’ 2})= 16m² -9

9+9 m^{’ 2}=16m² -9

18=7m²

m²=18/7

=±3 √2/7

Y= ±3 √2/7 x ±3 √1+18/7

Y=±3 √2/7 x ±15/√7

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