An ellipse of major axis 20*3^1/2 and minor axis 20 slides along the coordinate axes and always remains confined in the 1st quadrant. The locus of the centre of the ellipse therefore describes the arc of a circle. The length of this arc is? (a) 5pi (b)20pi (c)5pi/3 (d)20pi/3
solution-let S(x,y)and S(x,y)be the two foci of the ellipse.let (h,k) be the centre of the ellipse.
Also SS=2ae ,e is the eccentricity of the parabola.
since ellipse always slides between the coordinate axes and remains confined in first quadrant soX axes and Y axes will be tangent two this ellipse.therefore y,y and x,x are the perpendicular distances of foci from tangents.whose product is always b^2.
using all these values
this is the equation of circle with radius 20.
Centre will move on an arc as describe in the next diagram,of radius 20 and angle subtended at centre will be?/6 as angle on both side will be 30 degree.