Consider the parabola `(x-1)^(2)+(y-2)^(2)=((12x-5y+3)^(2))/(169)` and match the following lists :

Answer

`ator;btos;cto p;d to q`.

Explanation

`ator,btos,cto p,d to q`.
The locus of the point of intersection of perpendicular tangent is directrix, which is 12x-5y+3=0.
The parabola is symmetrical about its axis, which is a line passing through the focus (1,2) and perpendicular to the directrix. So, it has equation 5x+12y-29=0.
The minimum length of focal chord occurs along the latus rectum line, which is a line passing through the focus and parallel to the directrix, i.e., 12x-5y-2=0.
The locus of the foot of perpendicular from the focus upon any tangent is tangent at the vertex, which is parallel to directrix and equidistant from the directrix and latus rectum line.
Let the equation of tangent at vertex be
`12x-5y+lamda=0`
where `(|lamda-3|)/(sqrt(12^(2)+5^(2)))=(|lamda+2|)/(sqrt(12^(2)+5^(2)))orlamda=(1)/(2)`
Hence, the equation of tangent at vertex is 24x-10y+1=0.