an ellipse has major axis and minor axis lengths as 2a , 2b
let the foci be x1,y1 and x2,y2
and h,k be its center
and if it slides between co-ordinate axes such that it touches the x and y axis at all times
i)find the locus of one of the foci
ii)find the locus of the center
iii)the locus of the center id part of a circle ie an arc .... the angle subtended by thus ar at the origin is @
find cos@
1(2) let (h,k) be the centre
since the coordinate axis is touching the ellipse, origin is the point from which the two tangents are drawn.
now write general eq. (x-h)2/a2 +(y-k)2/b2=1
and then use T=0
sow homogenise T=0 with ellipse and put (coefficient of x2)+(coefficient of y2)=0
u will get the locus of centre
1i have got also one elegant method for (2)
hint: since the tangents are perpendicular therefore the locus of point of their intersection is the director circle of ellipse .
3but dude .... (x-h)2/a2 +(y-k)2/b2=1 is the equation og an ellipse whose center is at h.k but whose major axis is parallel to the co-ordinate axis ...... but this is not the case here na
19we get only an arc of a circle while tracing the locus of the centre
3organic that is given in the question only that it forms an ark!!. ......