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  • Find the set of values of ‘a’ and ‘b’, so that the equation <img alt="\mathrm{2 x^2+a y^2+4 x+b=0}" src="https://entrancecorner.oncodecogs

Find the set of values of ‘a’ and ‘b’, so that the equation \mathrm{2 x^2+a y^2+4 x+b=0} represents a circle

Option: 1

\mathrm{a=3, b \leq 3}


Option: 2

\mathrm{a=2, b \leqslant 3}


Option: 3

\mathrm{a=2, b \leqslant 2}


Option: 4

\mathrm{a \leqslant 2, \quad b=2}


Answers (1)

best_answer

For the given equation to represent a circle the  coefficients of \mathrm{x^{2}} and \mathrm{y^{2}} should be equal and \mathrm{{ }^{\prime} g^2+f^2-c \geq 0^{\prime}}

\mathrm{\Rightarrow \quad a=2, \quad 1-\frac{b}{2} \geq 0 \quad \Rightarrow a=2, b \leq 2 \text {. }}

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SANGALDEEP SINGH

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