Home
Class 11
MATHS
Consider an ellipse having its foci at A...

Consider an ellipse having its foci at `A(z_1)a n dB(z_2)` in the Argand plane. If the eccentricity of the ellipse be `e` an it is known that origin is an interior point of the ellipse, then prove that `e in (0,(|z_1-z_2|)/(|z_1|+|z_2|))`

Promotional Banner

Similar Questions

Explore conceptually related problems

If |z_(1)+z_(2)|=|z_1|+|z_2| then

If the roots of (z-1)^n=i(z+1)^n are plotted in an Argand plane, then prove that they are collinear.

For any two complex numbers z_1 and z_2 , prove that |z_1+z_2| =|z_1|-|z_2| and |z_1-z_2|>=|z_1|-|z_2|

Find the greatest and the least value of |z_1+z_2| if z_1=24+7ia n d|z_2|=6.

If z_1a n dz_2 are two complex numbers and c >0 , then prove that |z_1+z_2|^2lt=(1+c)|z_1|^2+(1+c^(-1))|z_2|^2dot

If z_1 and z_2 are two complex number such that |z_1|<1<|z_2| then prove that |(1-z_1 bar z_2)/(z_1-z_2)|<1

If a rg(z_1)=170^0a n d arg(z_2)=70^0 , then find the principal argument of z_1z_2dot

If (2z_1)/(3z_2) is purely imaginary then |(z_(1)-z_(2))/(z_(1)+z_(2))|

The region of argand diagram defined by |z-1|+|z+1|<=4 (1) interior of an ellipse (2) exterior of a circle (3) interior and boundary of an ellipse (4) none of these

If z_1a n dz_2 are complex numbers and u=sqrt(z_1z_2) , then prove that |z_1|+|z_2|=|(z_1+z_2)/2+u|+|(z_1+z_2)/2-u|