Let P be a point in the first quadrant lying on the ellipse $9x^2+16y^2=144,$such that the tangent at $P$ to the ellipse is inclined at an angle 135° to the positive direction of $x-$axis. Then the coordinates of $P$ are:

• A

  $\left(\frac{\sqrt{143}}{3}, \frac{1}{4}\right)$

• B

  $\left(\frac{8}{9}, \frac{\sqrt{77}}{3}\right)$

• C

  $\left(\frac{4}{\sqrt{2}}, \frac{3}{\sqrt{2}}\right)$

• D

  $\left(\frac{16}{5}, \frac{9}{5}\right)$