Can you find the cartesian equation for the locus of points #(x, y)# if #z=x+iy# and #|z+3| + |z-3| = 8#?
3 Answers
Explanation:
Considering
or
then with
squaring
or
The locus of the points is an ellipse
Explanation:
The modulus of a complex number
Therefore,
As,
Squaring both sides
Squaring both sides
This is the equation of an ellipse.
The reqd. Locus
Explanation:
Respected Cesareo R. Sir has solved the Problem using
Algebraic Method. We solve it with the help Geometry.
Let
With these, note that,
Now, by what is given,
Now, we know from Geometry that, under the condition
the variable pt.
its Eccentricity
Here, Length of Major Axis is
So,
Hence, the Ellipse is
Thus, the reqd. Locus
Enjoy Maths.!