Question

Tangents are drawn to the parabola `(x-3)^2+(y-4)^2=((3x-4y-6)^2)/(25)` at the extremities of the chord `2x-3y-18=0` . Find the angle between the tangents.

Answer 1

We have equation of parabola,
`sqrt((x-3)^(2)+(y+4)^(2))=(|3x-4y-6|)/(sqrt(3^(2)+(-4)^(2)))`
Focus of the parabola is (3,-4) and directrix is 3x-4y-6=0. The given chord 2x-3y-18=0 passes through the focus (3,-4) of the parabola. So, it is focal chord.
Since tangents drawn at the extremities of focal chord are perpendicular, angle between tangents is `90^(@)`.