If S(a, b) is a fixed point and P(alpha, beta | vedclass

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(B) The general equation of a parabola is defined as $PF^2 = e^2 PM^2$,where $e=1$ for a parabola.Given the equation $4[(x-a)^2+(y-b)^2]=(\alpha x+\be

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$\alpha^2+\beta^2=4$

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(B) The general equation of a parabola is defined as $PF^2 = e^2 PM^2$,where $e=1$ for a parabola.Given the equation $4[(x-a)^2+(y-b)^2]=(\alpha x+\beta y+7)^2$,we can rewrite it as:$(x-a)^2+(y-b)^2 = \left(\frac{\alpha x+\beta y+7}{2}\right)^2$To match the form $PF^2 = PM^2$,we normalize the line equation:$(x-a)^2+(y-b)^2 = \left(\frac{\alpha x+\beta y+7}{\sqrt{\alpha^2+\beta^2}}\right)^2 \cdot \frac{\alpha^2+\beta^2}{4}$For this to represent a parabola,the eccentricity $e$ must be $1$,which implies the coefficient $\frac{\alpha^2+\beta^2}{4} = 1^2$.Therefore,$\alpha^2+\beta^2=4$.

If $S(a, b)$ is a fixed point and $P(\alpha, \beta)$ is a variable point such that $4[(x-a)^2+(y-b)^2]=(\alpha x+\beta y+7)^2$ represents a parabola,then the locus of $P(\alpha, \beta)$ is

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