JEE PYQ: Circle Question 28
Question 28 - 2019 (10 Apr Shift 1)
If the circles $x^2 + y^2 + 5Kx + 2y + K = 0$ and $2(x^2 + y^2) + 2Kx + 3y - 1 = 0$, $(K \in \mathbb{R})$, intersect at the points $P$ and $Q$, then the line $4x + 5y - K = 0$ passes through $P$ and $Q$, for:
(1) infinitely many values of $K$
(2) no value of $K$
(3) exactly two values of $K$
(4) exactly one value of $K$
Show Answer
Answer: (2)
Solution
Radical axis: $S_1 - S_2 = 0$ gives $4Kx + \frac{1}{2}y + K + \frac{1}{2} = 0$. Comparing with $4x + 5y - K = 0$: $K = \frac{1}{10}$ and $-2K = 10K + 10$, which are inconsistent. No value of $K$.
BETA
