The line x+y=2 intersects the curve (x^(2))/(16)+(y^(2))/(9)=1 at A B. A circle with diameter AB is drawn to intersects (x^(2))/(1

The line x+y=2 intersects the curve (x^(2))/(16)+(y^(2))/(9)=1 at A B. A circle with diameter AB is drawn to intersects (x^(2))/(16)+(y^(2))/(9)=1 at two more points C and D .If the equation of line CD is y=mx+c which touches the curve x^(2)=8y then the value of |c| is equal to​

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