If x-y=1 is a tangent to the hyperbola x² 4 - y² 3 =1 , then the point of contact is

Step-by-step solution

Given, x-y=1 and x² 4 - y² 3 =1 Put y=x-1 from Eq. (i) in Eq. (ii), we get aligned & & x² 4 - (x-1)² 3 &=1 & & 3 x²-4(x-1)² 12 &=1 & & 3 x²-4 (x²+1-2 x ) &=12 & & 3 x²-4 x²-4+8 x &=12 & &-x²+8 x-16 &=0 & & x²-8 x+16 &=0 & &x-4)² &=0 & & x &=4,4 aligned Put x=4 in Eq. (i), we get aligned 4-y &=1 y &=3 The point of contact &=(4,3) aligned