Find the equation of the ellipse referred to its centre as the origin and major axis as the X-axis give that (iii) major axis is of length 26 and foci are (`!=`12, 0)

Find the equation of line in space parallel to X-axis and passing through the origin

Find the equation of the parabola whose vertex is at the origin, axis is along the X-axis and the length of the latus rectum is 4 units.

Find the differential equation of the family of all circles touching the chi -axis at the origin.

Find the equation of an cllipse in its standard form with major axis X-axis and minor axis along Y-axis when the distance between the foci is 2 units and that between the directrices is 4 units.

Find the equation to the locus of a point whose distance from the X-axis is double its distance from the Y-axis.

The foci of an ellipse with its centre as the origin are ( != 3, 0) and e = 1/2. Find the length of the minor axis and the equation of the clipse.

Find the equation of the straight line which cuts the Y-axis at the point (0, -2) making an angle of 30^@ with OX.

Write down the equation of the straight line passing through the origin which makes an angle 60^@ with positive x-axis.