# A parabola with focus $(-1,-1)$ is tangent to $y=3x-8$ at $(7,13)$. Find the latus rectum. [duplicate]

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

## marked as duplicate by amd, HK Lee, Claude Leibovici, Chris Custer, Martin SleziakMay 11 '18 at 11:20

• I tried the parabola of the form $x^2=4ay$ considering that (7,13) lies on parabola and focus us (-1,-1) – Samar Imam Zaidi May 11 '18 at 4:34
• But not getting the equation of parabola – Samar Imam Zaidi May 11 '18 at 4:35
• Let $(p,q)$ be the vertex, what is the equation of directrix & that of the parabola – lab bhattacharjee May 11 '18 at 4:44
• Why do you think the parabola’s axis is vertical? – amd May 11 '18 at 6:29