Question

The circle passing through the point $(–1,0)$ and touching the $y-$axis at $(0,2)$ also passes through the point

• A. Option a missing
• B. $(-4,0)$
• C. Option b missing
• D. Option c missing

Answer 1

The correct option is B $(-4,0)$


The equation of the circle directing $y-$axis at $(0,2)$ can be put in the form
$(x–h{)}^2+(y–2{)}^2=h^2$
which will pass through $(–1,0)$ if
$(–1–h{)}^2+4=h^2$
$\Rightarrow h=-\frac{5}{2}$
Thus the equation of the circle is
${(x+\frac{5}{2})}^2+(y-2{)}^2={\left(\frac{5}{2}\right)}^2$
which passes through $(-4,0)$