Question

$A$: lf the circles $x^2+y^2=a^2,$ $x^2+y^2-6x-8y+9=0$ touch externally then $a=1$
$R$: Two circles with centres $C_1,C_2$ and radii $r_1,r_2$ respectively touch externally iff $C_1{C}_2=r_1+r_2$

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is not the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Answer 1

The correct option is A Both A and R are true and R is the correct explanation of A

$A:S_1:x^2+y^2=a^2$
$C_1:(0,0)r_1=a$
$S_2:x^2+y^2-6x-8y+9=0$
$C_2\equiv (3,4)r_2=4$
$S_1$ and $S_2$ touches externally.
$r_1+r_2=C_1{C}_2$
$a+4=5$
$A=1$ True.
R: Is True (concept)
Both A & R are True and R is correct explanation of A