Question

If the length of the chord of the circle, x + y² = r²(r > 0) along the line, y – 2x = 3 is r, then r² is equal to ______.

Options

• `9/5`

• 12

• `24/5`

• `12/5`

Answer 1

If the length of the chord of the circle, x + y² = r²(r > 0) along the line, y – 2x = 3 is r, then r² is equal to `underlinebb(12/5)`.

Explanation:

In right ΔRSQ, sin 60° = `(RS)/r`

⇒ RS = `r xx sqrt(3)/2 = (sqrt(3)r)/2` 

Now equation of PQ is y – 2x – 3 = 0

∴ `(sqrt(3)r)/2 = (|0 + 0 -3|)/sqrt(5)`

⇒ `(sqrt(3)r)/2 = 3/sqrt(5)`

⇒ r = `(2sqrt(3))/5`

⇒ r² = `12/5`