An ellipse having length of semi major and minor axes 7 and 24 respectively slides between the coordinate axes. If its centre be `(alpha, beta)` then `alpha^2 + beta^2 `=

An ellipse with major and minor axis 6sqrt3 and 6 respectively, slides along the coordinates axes and always remains confined in the first quardrant. If the length if arc decribed by center of ellipse is (pilambda)/6 then the value of lambda is

An ellipse having semi major and minor axes 24 and 7 slieds between two lines at right angles to one another. If A be the area enclosed by the locus of the centre of the ellipse then 10/pi A=

An ellipse hase semi-major of length 2 and semi-minor axis of length 1. It slides between the coordinates axes in the first quadrant while mantaining contact with both x-axis and y-axis. The locus of the centre of the ellipse is

If the normal at any point P on the ellipse cuts the major and minor axes in G and g respectively and C be the centre of the ellipse, then

The equation of the plane which makes with coordinate axes, a triangle with its centroid (alpha, beta , gamma) is

If alpha , beta are the roots of ax ^2 + bx +c=0 then alpha ^5 beta ^8 + alpha^8 beta ^5=

A line makes angles alpha,beta and gamma with the coordinate axes. If alpha+beta=90^0, then find gamma .

A line makes angles alpha,betaa n dgamma with the coordinate axes. If alpha+beta=90^0, then find gammadot

For the ellipse 4(x - 2y + 1)^2 +9(2x+y+ 2)^2 = 180 , lengths of major and minor axes are respectively

The eccentricity of an ellipse is 1/2 and the distance between its foci is 4 units. If the major and minor axes of the ellipse are respectively along the x and y axes, find the equation of the ellipse