JEE PYQ: Circle Question 22
Question 22 - 2020 (09 Jan Shift 1)
A circle touches the $y$-axis at the point $(0, 4)$ and passes through the point $(2, 0)$. Which of the following lines is not a tangent to this circle?
(1) $4x - 3y + 17 = 0$
(2) $3x - 4y - 24 = 0$
(3) $3x + 4y - 6 = 0$
(4) $4x + 3y - 8 = 0$
Show Answer
Answer: (4)
Solution
Circle: $(x-0)^2 + (y-4)^2 + \lambda x = 0$. Through $(2,0)$: $4 + 16 + 2\lambda = 0 \Rightarrow \lambda = -10$. Circle: $x^2 + y^2 - 10x - 8y + 16 = 0$. Center $(5,4)$, $r = 5$. Distance from center to $4x + 3y - 8 = 0$: $\frac{|20+12-8|}{5} = \frac{24}{5} \neq 5$. Not tangent.
BETA
