Let y=3x−8 be the equation of the tangent at the point  (7, 13) lying on a parabola whose focus is at (−1,−1) . The  length of the latus rectum of the parabola is

The image of focus (−1,−1) upon the tangent y=3x−8 is the point (5,−3) . It will lie on the directrix.  Slope of directrix =−7−513+3=−18Its equation isy+3=−18(x−5) or  x+8y+19=0∴  Latus rectum =2×( Distance of focus from directrix )=2×|−1−8+19|65=2065