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# ellipses

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Let $$F_1 = (0,1)$$ and $$F_ 2= (4,1)$$. Then the set of points  such that $$PF_1 + PF_2 = 6$$ form an ellipse. The equation of this ellipse can be written as $$\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1.$$ Find $$h + k + a + b.$$

Oct 4, 2021

$h + k + a + b = 8 + 2 \sqrt{3}$.