A circle touches the y-axis at the point 0 , 4 and passes through the point 2 , 0 . Which of the following…

1. $4x-3y+17=0$
2. $3x-4y-24=0$
3. $3x+4y-6=0$
4. $4x+3y-8=0$

Solution

Equation of family of circle
${\left(x-0\right)}^2+{\left(y-4\right)}^2+\lambda x=0$ $\Rightarrow passes\left(2,0\right)$
$4+16+2\lambda =0\Rightarrow \lambda =-10$
$x^2+y^2-10x-8y+16=0$
Centre $\left(\mathrm{5,4}\right),R=\sqrt{25+16-16}=5$
Check the options.
Option (4)
$\left|\frac{4\times 5+3\times 4-8}{5}\right|=\frac{24}{5}\ne 5$

Asked in: JEE Main 2020 (09 Jan Shift 1)

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