JEE MAIN - Mathematics (2020 - 5th September Evening Slot - No. 14)
If the length of the chord of the circle,
x2 + y2 = r2 (r > 0) along the line, y – 2x = 3 is r,
then r2 is equal to :
x2 + y2 = r2 (r > 0) along the line, y – 2x = 3 is r,
then r2 is equal to :
$${9 \over 5}$$
$${{24} \over 5}$$
$${{12} \over 5}$$
12
Explanation
_5th_September_Evening_Slot_en_14_1.png)
In right $$\Delta $$CDB,
sin 60o = $${{CD} \over r}$$
$$ \Rightarrow $$ CD = $$r \times {{\sqrt 3 } \over 2}$$ = $${{\sqrt 3 r} \over 2}$$
Now equation of AB is
y – 2x – 3 = 0
So $${{\sqrt 3 r} \over 2}$$ = $${{\left| {0 + 0 - 3} \right|} \over {\sqrt 5 }}$$
$$ \Rightarrow $$ $${{\sqrt 3 r} \over 2}$$ = $${3 \over {\sqrt 5 }}$$
$$ \Rightarrow $$ r = $${{2\sqrt 3 } \over 5}$$
$$ \Rightarrow $$ r2 = $${{12} \over 5}$$
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