The centre of the sphere alpha ,r^2 - 2u cdot | vedclass

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Question

(A) The given equation of the sphere is $\alpha \,r^2 - 2u \cdot r = \beta$. Dividing the entire equation by $\alpha$ (since $\alpha 
e 0$),we get: $

Vedclass · Accepted Answer

$u/\alpha$

Vedclass · Answer

(A) The given equation of the sphere is $\alpha \,r^2 - 2u \cdot r = \beta$. Dividing the entire equation by $\alpha$ (since $\alpha 
e 0$),we get: $r^2 - \frac{2}{\alpha} u \cdot r = \frac{\beta}{\alpha}$. Comparing this with the standard vector equation of a sphere $r^2 - 2a \cdot r = c$,where $a$ is the position vector of the centre,we have: $2a = \frac{2}{\alpha} u$. Therefore,$a = \frac{u}{\alpha}$. Thus,the centre of the sphere is $u/\alpha$.

The centre of the sphere $\alpha \,r^2 - 2u \cdot r = \beta ,(\alpha \ne 0)$ is

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