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# If the centre of the ellipes is $(4 , -2 )$ and one of the focus is $(4 , 2 ),$ find the other focus?

Toolbox:
• If a point moves so that the sum of its distances from the fixed points is a constant,then the path traced as an ellipse with major axis of length equal to the constant sum and foci at the two fixed points.
Step 1:
The centre is at $C(4,-2)$ and one focus is $F(4,2)$.Let $F'(x_1,y_1)$ be the other focus.
Now $C$ is the midpoint of $FF'$.
Step 2:
Therefore $\large\frac{4+x_1}{2}$$=4 \large\frac{2+y_1}{2}$$=-2$
(i.e)$x_1=4,y_1=-6$
The other focus is $(4,-6)$