an ellipse has eccentricity 1/2 and a focus at the point p(1/2,1).One of its directrix is the common tangent near to the point P to the circle x^2+y^2=1 and hyperbola x^2-y^2=1 the equation of ellipse is
i have drawn figure but unable to proceed further
You need to have a sound background to answer this one.
Equation of tangent to the given circle is and that of the given hyperbola is .
If they both constitute the same line them and thus
The common tangent will be a line parallel to and such a line can only be
Since we are interested in the directrix nearer to the point the equation of the directrix will be .
The general equation of any conic is
where is the focus of the conic, the eccentricity and the directrix of the conic
Thus the required equation is