A point moving around circle `(x + 4)^2 + (y +2)^2 =25` with centre C broke away from it either at the point A or point B on the circle and move along a tangent to the circle passing through the point D(3,-3). Find the following: (a) Equation of the tangents at A and B. (b) Coordinates of the points A and B. (c) Angle ADB and the maximum and minimum distances of the point D from the circle. (d) Area of quadrilateral ADBC and the `Delta`DAB. e) Equation of the circle circumscribing the `DeltaDAB` and also the intercepts made by the this circle on the coordinates axes.

Answer

`x^(2) + y^(2) + x + 5y – 6`, x intercept 5; y intercept 7