Origin is shifted to $(\frac{9}{2}, p)$ . If the new equation of the locus $y^{2} + 2 x - 8 y + 7 = 0$ does not contain a term in Y, then p =

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Solution

The correct option is B 4
(0,0) shifted to $(\frac{9}{2}, p)$
Let (x,y) be co-oridinates in original co-ordinate system
and (x,y) be co-ordinates in new co-ordinate system
Relation between co-ordinate systems:
$x - \frac{9}{2} = X \Rightarrow x = X + \frac{9}{2}$
$y - P = Y \Rightarrow y = Y + P$
$y^{2} + 2 x - 8 y + 7 = 0$ will transfrom to
$(Y + P)^{2} + 2 (X + \frac{9}{2}) - 8 (Y + P) + 7 = 0$
The above equation should not have Y term
$\Rightarrow$ coefficient of y = 0
$\Rightarrow 2 P - 8 = 0$
$\Rightarrow P = 4$

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