Question

Length of intercept made by line x + y = 2 on the circle x² + y² – 4x – 6y – 3 = 0 is ______.

Options

• `2sqrt(23)`

• `sqrt(23)`

• `sqrt(46)`

• `4sqrt(23)`

Answer 1

Length of intercept made by line x + y = 2 on the circle x² + y² – 4x – 6y – 3 = 0 is `underlinebb(sqrt(46))`.

Explanation:

Where a is radius of circle and p is length of perpendicular

p = `(2 + 3 - 2)/sqrt(2) = 3/sqrt(2)` and a = `sqrt(4 + 9 + 3)` = 4

∴ Length of intercept = `2sqrt(a^2 - p^2)`

= `2sqrt((4)^2 - (3/sqrt(2))^2)`

= `2sqrt(16 - 9/2)`

= `2sqrt((32 - 9)/2)`

= `2sqrt(23/2)`

= `sqrt(2).sqrt(23)`

= `sqrt(46)`