Class 11

Math

Co-ordinate Geometry

Conic Sections

The auxiliary circle of a family of ellipses passes through the origin and makes intercepts of 8 units and 6 units on the x and y-axis, respectively. If the eccentricity of all such ellipses is $21 ,$ then find the locus of the focus.

let focus be $(h,k)$

let distanc of focus from centre = al

al = $(h−4)_{2}+(k−3)_{2} $

a = radius of ac = 5

$(25 )=(h−4)_{2}+(k−3)_{2} $

$(25 )_{2}=(h−4)_{2}+(k−3)_{2}$

$(x−4)_{2}+(y−3)_{2}=425 $