A common tangent to 9 x²-16 y²=144 and x²+y²=9 , is

Step-by-step solution

Let y=m x+c be a common tangent to 9 x²-16 y²=144 and x²+y²=9 . Since, y=m x+c is a tangent to 9 x²-16 y²=144 c²=a² m²-b² c²=16 m²-9 (i) Now, y=m x+c is a tangent to x²+y²=9 c m²+1 =3 c²=9 (1+m² ) From Eqs. (i) and (ii), we get 16 m²-9=9+9 m² m= 3 2 7 On putting the value of m in Eq (ii), we get c= 15 7 Hence, y=3 2 7 x+ 15 7 is a common tangent.