Question

The equation of circle with centre $(-4,3)$ and touching the circle $x^2+y^2=1$, is

• A. $x^2+y^2+8x-6y+9=0$
• B. $x^2+y^2+8x+6y-11=0$
• C. $x^2+y^2+8x+6y-9=0$
• D. $Noneofthese$

Answer 1

The correct option is A $x^2+y^2+8x-6y+9=0$

R.E.F image

center of $x^2+y^2=1$=(0,0)radius=1

Form figure $,{00}^{\prime }=r+r_2$

$\Rightarrow \sqrt{(-4{)}^2+(3{)}^2}=1+r_2$

$\Rightarrow \sqrt{16+9}=r_2+1\Rightarrow r_2=5-1=4$

$\to$ Equation:$(x+4{)}^2+(y-3{)}^2=16$

$\Rightarrow x^2+y^2+8x-6y+9=0\Rightarrow \left(A\right)$