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$y^{2} = 16 x$ is a parabola and $x^{2} + y^{2} = 16$ is a circle . Then

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circle passes through the vertex of the parabola

circle touches the parabola at the vertex

circle passes through the focus of the parabola

circle lies inside the parabola.

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detailed solution

Correct option is C

Centre of the circle is the origin, the vertex of the parabola and the focus of the parabola is A (4, 0). The circle passes through A.

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y2=16x is a parabola and x2+y2=16 is a circle . Then

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$y^{2} = 16 x$ is a parabola and $x^{2} + y^{2} = 16$ is a circle . Then