Let y2 = 16x be a given parabola and L be an extremity of its latus rectum in the first quadrant. If a chord is drawn through L with slope-1, then the length of this chord is:

Equation of the latus rectum is x = 4 and the coordinates of L are (4, 8). Equation of the chord through L with slope-1 is y−8=−(x−4) ⇒x+y=12Solving the equation of the chord and the parabola we get y2=16(12−y)⇒y=8 and -24So the coordinates of M the other end of the chord through L is (36, –24). and LM=(36−4)2+(−24−8)2=322