Consider a parabola with vertex $A$. Let $P,Q$ be two points on it. The equations of tangents at $P,Q,A$ to the parabola are $3x+4y-7=0,2x+3y-10=0$ and $x-y=0$ respectively, then which is/are correct?

Let the tangent at the vertex A meets the tangents at P and Q in L and M
$\therefore \mathrm{L}(1,1),\mathrm{M}(2,2)$
Let S be the focus of the parabola
equation of SL is 4x – 3y – 1 = 0
equation of SL is 3x – 2y – 2 = 0
$\therefore \mathrm{S}=(4,5),\mathrm{A}\left(\frac{{\displaystyle 9}}{{\displaystyle 2}},\frac{{\displaystyle 9}}{{\displaystyle 2}}\right), \mathrm{length} \mathrm{of} \mathrm{LR}=4\mathrm{A}=2\sqrt{2}$

$\mathrm{SA}=\mathrm{a}=\frac{1}{\sqrt{2}}$
Equation of axis is x + y – 9 = 0