Question

Equation of the circle of radius $5$ whose centre lies on y-axis in first quadrant and passes through $(0,1)$ is?

• A. $x^2+y^2-12y+11=0$
• B. $x^2+y^2-6y-1=0$
• C. $x^2+y^2-8y+3=0$
• D. $Noneofthese$

Answer 1

Answer: (A)

$x^2+y^2-12y+11=0$

Radius ,$r=5$

Let the center of circle be $(0,y)$

$E$ qn of circle:- $(x-o{)}^2+(y-y{)}^2=25$

The circle passes through $(0,1)$

substituting $(0,1)$ is place of $(x,y)$

$(8-0{)}^2+(1-y-1{)}^2=25$

Taking square root

$1-y_1=\pm 5$

$y_1=-4$ or $6$

$A$ is circle is in first quadrant

$y_1$ cannot be $-4$

$E$ an of circle:-

$x^2+(y-6{)}^2=25$

$x^2+y^2-12y+11=0$

Ans is option $A$