A plane passes through a fixed point (a, b, c) and cuts the axes in A,...

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A plane passes through a fixed point (a, b, c) and cuts the axes in A, B, C. Show that the locus of the centre of the sphere OABC is a/x+b[y+c/z32. [Allahabad, 1981] A sphere of constant radius a passes through the origin meets the axes in A, B. C. Prove that the centroid of the triangle ABC lies on the sphere and 9(x1+2)=D4a². [Allahabad, 1980] %3D ah the origin A plane passes through a fixed point (a, b, c) and cuts the axes in A, B, C. Show that the locus of the centre of the sphere OABC is a/x+b[y+c/z32. [Allahabad, 1981] A sphere of constant radius a passes through the origin meets the axes in A, B. C. Prove that the centroid of the triangle ABC lies on the sphere and 9(x1+2)=D4a². [Allahabad, 1980] %3D ah the origin

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r y the locus of the Contre a the sphore O AGC let the Points ttt... View the full answer