JEE PYQ: Circle Question 19
Question 19 - 2020 (05 Sep Shift 2)
If the length of the chord of the circle, $x^2 + y^2 = r^2$ $(r > 0)$ along the line, $y - 2x = 3$ is $r$, then $r^2$ is equal to:
(1) $\frac{9}{5}$
(2) $12$
(3) $\frac{24}{5}$
(4) $\frac{12}{5}$
Show Answer
Answer: (4)
Solution
Distance from origin to line $= \frac{3}{\sqrt{5}}$. Half-chord $= \frac{r}{2}$. So $\frac{9}{5} + \frac{r^2}{4} = r^2 \Rightarrow \frac{3r^2}{4} = \frac{9}{5} \Rightarrow r^2 = \frac{12}{5}$.
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