Question Number 32679 by rahul 19 last updated on 31/Mar/18
$${If}\:\mathrm{4}{a}^{\mathrm{2}} −\mathrm{5}{b}^{\mathrm{2}} +\mathrm{6}{a}+\mathrm{1}=\mathrm{0}\:{and}\:{the}\:{line} \\ $$$${ax}+{by}+\mathrm{1}=\mathrm{0}\:{touches}\:{a}\:{fixed}\:{circle} \\ $$$${then}\:{the}\:{correct}\:{statement}\:{is}\:: \\ $$$$\left.\mathrm{1}\right)\:{centre}\:{of}\:{circle}\:{is}\:{at}\:\left(\mathrm{3},\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{radius}\:{of}\:{circle}\:{is}\:\sqrt{\mathrm{3}}. \\ $$$$\left.\mathrm{3}\right)\:{circle}\:{passes}\:{through}\:\left(\mathrm{1},\mathrm{0}\right). \\ $$$$\left.\mathrm{4}\right)\:{none}\:{of}\:{these}. \\ $$