The eccentricity of ellipse `ax^2 + by^2 + 2gx + 2fy + c = 0` if its axis is parallel to x-axis is

The circle x^(2) + y^(2) + 2g x + 2fy + c = 0 does not intersect the y-axis if

Find the centre and radius of the circle ax^(2) + ay^(2) + 2gx + 2fy + c = 0 where a ne 0 .

If the pair of lines ax^2 +2hxy+ by^2+ 2gx+ 2fy +c=0 intersect on the y-axis then

the equation ax^(2)+ 2hxy + by^(2) + 2gx + 2 fy + c=0 represents an ellipse , if

Find the eccentricity of the ellipse whose latus rectum is (i) half its major axis, (ii) half its minor axis.

Find the equation of the ellipse whose centre is (-2,3) and whose semi axes are 3 and 2 when major axis is (i.) parallel to x-axis (ii.) parallel to y-axis.

For equation of the curve whose subnormal is constant, then (a) its eccentricity is 1 (b) its eccentricity is sqrt(2) (c) its axis is the x-axis (d)its axis is the y-axis.

Find the eccentricity of an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 whose latus rectum is half of its major axis.

the eccentricity of an ellipse (x^(2))/(a^(2))+(y^(2))=1 whose latus rectum is half of its minor axes , is

The eccentricity of an ellipse with centre at the orgin and axes along the coordinate axes , is 1/2 if one of the directrices is x=4, the equation of the ellipse is