Find the equation of the tangen to the curve y the square r

Find the equation of the tangen to the curve y = the square root of 2x^2+1 which passes through the point (5,7). Hint notice that the point (5,7) is not on the graph of the curve y = the square root of 2x^2+1. Proceed and denote the point where the line touches the curve by (h,k). Use the data in the problem to find h and k

Solution

y =2x^2+1 dy/dx= 4x for tangent dy/dx of that point on curve it is 0 so x=0 putting x=0 in equation y=1 so now equation of line passing through (0,1) and (5,7) y-1 = (6/5) x