A) \[a{{\alpha }^{2}}+a{{\beta }^{2}}-{{r}^{2}}\]
B) \[{{\alpha }^{2}}+{{\beta }^{2}}-\frac{{{r}^{2}}}{a}\]
C) \[{{\alpha }^{2}}+{{\beta }^{2}}+\frac{{{r}^{2}}}{a}\]
D) \[{{\alpha }^{2}}+{{\beta }^{2}}-{{r}^{2}}\]
Correct Answer: B
Solution :
Length of tangent is\[\sqrt{{{S}_{1}}}\]. Equation of circle is \[{{x}^{2}}+{{y}^{2}}-\frac{{{r}^{2}}}{a}=0\] Hence\[{{S}_{1}}={{\alpha }^{2}}+{{\beta }^{2}}-\frac{{{r}^{2}}}{a}\].
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