A normal is drawn at the point $$P$$ to the circle $$x^2+y^2=25$$, which is inclined at $$45^{\circ}$$ with the straight line $$y=6$$. Then, the point lies on the straight line

If a tangent to the circle $$x^2+y^2=1$$ intersect the co-ordinate axes at distinct points $$P$$ and $$Q$$, then the locus of the mid-point of $$P Q$$ is

The locus of the mid-point of the chord if contact of tangents drawn from points lying on the straight line $$4x - 5y = 20$$ to the circle $${x^2} + {y^2} = 9$$ is

Equation of circle which passes through the points (1, $$-$$2) and (3, $$-$$4) and touch the X-axis is