JEE PYQ: Circle Question 27
Question 27 - 2019 (09 Apr Shift 2)
The common tangent to the circles $x^2 + y^2 = 4$ and $x^2 + y^2 + 6x + 8y - 24 = 0$ also passes through the point:
(1) $(4, -2)$
(2) $(-6, 4)$
(3) $(6, -2)$
(4) $(-4, 6)$
Show Answer
Answer: (3)
Solution
$C_1(0,0), r_1 = 2$; $C_2(-3,-4), r_2 = 7$. $C_1C_2 = 5 = r_2 - r_1$: internal tangency. Common tangent: $S_1 - S_2 = 0 \Rightarrow 6x + 8y - 20 = 0 \Rightarrow 3x + 4y = 10$. $(6,-2)$: $18 - 8 = 10$. Verified.
BETA
