A common tangent to the conics x^2=6 y and 2 x^2-4 y^2=9 is:

Step-by-step solution

aligned &x^2-6 y &2 x^2-4 y^2=9 aligned Consider the line, x-y= 3 2 On solving (i) and (iii), we get only x=3, y= 3 2 Hence (3, 3 2 ) is the point of contact of conic (i), and line (iii) On solving (ii) and (iii), we get only x=3 , y= 3 2 Hence (3, 3 2 ) is also the point of contact of conic (ii) and line (iii). Hence line (iii) is the common tangent to both the given conics.