The largest value of k for which the circle x^2 +y^2 =k^2 lies completely in the interior of the parabola y^2 =4x+16 ?


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Question Number 148991 by gsk2684 last updated on 02/Aug/21

$T h e l a r g e s t v a l u e o f k f o r w h i c h$ $t h e c i r c l e x^{2} + y^{2} = k^{2} l i e s c o m p l e t e l y$ $i n t h e i n t e r i o r o f t h e p a r a b o l a$ $y^{2} = 4 x + 16 ?$
	Answered by mr W last updated on 02/Aug/21

	$x^{2} + 4 x + 16 - k^{2} = 0$ $Δ = 4^{2} - 4 (16 - k^{2}) ⩽ 0$ $k^{2} ⩽ 12$ $\Rightarrow - 2 \sqrt{3} ⩽ k ⩽ 2 \sqrt{3}$
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