Question

Assertion :Consider circles $C_1\equiv x^2+y^2-6x-4y+9=0$ and $C_2\equiv x^2+y^2-8x-6y+23=0$
Circle $C_1$ bisects the circumference of the circle $C_2$ Reason: Centre of $C_1$ lie on $C_2$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Statement-1
$S_1\equiv x^2+y^2-4=0$ $\Rightarrow C_1(0,0),r_1=2$
$S_2\equiv x^2+y^2-8x+7=0$ $\Rightarrow C_2(4,0),r_2=3$
Now, $C_1{C}_2=4$
$r_1+r_2=5,|r_1+r_2|=1$
$|r_1-r_2|<C_1{C}_2<r_1+r_2$
$\therefore$ circle intersect each other
Statement-2 is obviously false.
Ans: B