Find the equation to the ellipse, whose focus is the point `(-1,1),`whose directrix is the straight line `x-y +3=0,` and whose eccentricity is `1/2.`

Find the equation of the ellipse whose focus is S(+-1, -1), the corresponding directrix is x -y+3=0, and eccentricity is 1/2. Also find its center, the second focus, the equation of the second directrix, and the length of latus rectum.

Find the equation of the ellipse whose vertices are (+-13,0) and foci are (+-5,0)

Find the equation of the circle passing through the points (2,3) and (-1,-1) and whose centre is on the line x-3y-11=0.

Find the equation of the ellipse whose one of the foci is (2,0) and the corresponding directrix is x = 8 and eccentricity is (1)/(2) .

Find the length of the latus rectum of the parabola whose focus is at (2, 3) and directrix is the line x-4y+3=0 .

Find the equation of the circle which passes through the points (1,-2),(4,-3) and whose center lies on the line 3x+4y=7.

Find the equation of the circle passing through the point (4,1) and (6,5) and whose centre is on the line 4x + y = 16 .

Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre is on the line 4x+y=16 .

Find the coordinates of any point on the parabola whose focus is (0, 1) and directrix is x+2=0

Find the equation of a circle which passes through the points (1,-2) and (4,-3) and whose centre lies on the line 3x+4y=0