A is a point (1,3,4) and B is the point (1, -2, -1). A point P moves so that3PA = 2PB. Prove that locus of P is the spherex^2 + y^2 + z^2 - 2x - 14y - 16z +42 = 0.​

I may use the 'splitting of middle terms' method which is most similar to the 'long division' method.

A is a point (1,3,4) and B is the point (1, -2, -1). A point P moves so that

3PA = 2PB. Prove that locus of P is the sphere

x^2 + y^2 + z^2 - 2x - 14y - 16z +42 = 0.

So it's divisible.

Okay. Let me use the 'long division' method too. Please see the attachment.

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Thank you. Have a nice day. :-)