angle between thetangent to the parabola y2=4ax at the pointwhere intersect with the line x-y-a=0

Solve the two equations and get the intersecting points.

(ii) Then apply the point form of tangent equation to get the equations of two tangents. (iii) Then find the solve of the two lines and then finally use the following formula

tan(theta) = modulas (m1-m2 / 1 +m1m2) To get the angle between the tangents.

 

2. From the given equation of parabola, you can easly get the coordinates of focus. Using focus point and angle of focal chord you can get the equation of it and solve these with equation of parabola to get the intersecting points. Then finally apply the distance formula to find its length. \