Multiple choice

If the equation of a given circle is ${ x }^{ 2 }+{ y }^{ 2 }=36$, then the length of the chord which lies along the line $3x+4y-15=0$

  1. $3\sqrt { 6 } $
  2. $2\sqrt { 3 } $
  3. $6\sqrt { 3 } $

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The distance d from the center (0,0) to the line 3x+4y-15=0 is |3(0)+4(0)-15| / sqrt(3^2+4^2) = 15/5 = 3. The radius r is 6. The chord length is 2 * sqrt(r^2 - d^2) = 2 * sqrt(36 - 9) = 2 * sqrt(27) = 2 * 3 * sqrt(3) = 6 * sqrt(3).

AI explanation

For the circle x^2+y^2=36, the radius r is 6. The perpendicular distance from the center (0,0) to the line 3x+4y-15=0 is calculated as |3(0) + 4(0) - 15| / sqrt(3^2 + 4^2) = 15/5 = 3. Using the chord length formula 2 * sqrt(r^2 - d^2), the length is 2 * sqrt(36 - 9) = 2 * sqrt(27) = 6 * sqrt(3).

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