1) P(x,y)is a moving point Cartesian Coordinates such that the sum of the distance of the point p from the point(4,0) and the distance of P from the origin is 8 units. Show that the locus of P is an ellipse.State the coordinates of the center,vertices and foci of the ellipse and sketch the ellipse.
2) Find the perpendicular distance from the centre of the circle x2+y2-8x+2y+8=0 to the straight line 3x+4y=28.Hence,find the shortest distance between the circle and the straight line.

Do the math and graph the results.