Locus of intersection of tangents if angle between tangent is theta

Centre of locus of point of intersection of tangent to y^2 = 4ax, if the angle between tangents is 45^@ is

Centre of locus of point of intersection of tangent to y^(2)=4ax, if the angle between tangents is 45^(@) is

The locus of point of intersection of tangents inclined at angle 45^@ to the parabola y^2 = 4x is

The locus of point of intersection of tangents inclined at angle 45^(@) to the parabola y^(2)=4x is

Equation of tangent at a point | Equation of tangent from a point | Angle between tangents

The locus of point of intersection of tangents to the ellipse.If the difference of the eccentric angle of the points is theta

The locus of the point of intersection of tangents to the circle x=a cos theta, y=a sin theta at points whose parametric angles differ by pi//4 is