The co-ordinates of focus and its nearest vertex of an ellipse are (3, -5) and (4, -5) respectively and eccnetricity is 2/3 . Find the co ordinate of its centre and the co-ordinate of the point of contact of. the directrix and Major axis nearest to focus.

Find the co-ordinates of the point of intersection of the equation 2x-3y=12 on the y-axis.

Determine the co-ordinates of the point intersection of the equation 2x+3y=12 on the x-axis.

The eccentricity of an ellipse is (2)/(3) and the coordinates of its focus and the corresponding vertex are (1,2) and (2,2) respectively. Find the equation of the ellipse . Also find the coordinate of the point of intersection of its major axis and the directrix in the same direction .

Find the cartesian co-ordinates of the points whose polar co-ordinates are (5,pi/4)

Find the co-ordinate of a point on the circle x^2 +y^2 - 4x + 2y - 20 = 0 nearest to (2, 3/2) .

Find the cartesian co-ordinates of the points whose polar co-ordinates are (3,pi/2)

(a) Find the polar co-ordinates of a point Cartesian co-ordinates are (-1,1) .

Find the cartesian co-ordinates of the points whose polar co-ordinates are (3,pi/6)

Find the cartesian co-ordinates of the points whose polar co-ordinates are (2,pi/2)

Find the cartesian co-ordinates of the points whose polar co-ordinates are (1,pi)