Question

Let the equation of circle is `x^(2) + y^(2) - 6x - 4y + 9 = 0` . Then the line 4x + 3y - 8 = 0 is a
A. tangent of the circle
B. normal of the circle
C. chord of the angle
D. None of the above

Answer 1

Correct Answer - A
Given circle is `x^(2) + y^(2) - 6x - 4y + 9 = 0`
C( 3, 2) , r = 2
If line 4x + 3y - 8 = 0 is a tangent to the circle , then
`|(4(3) + 3(2) - 8)/(sqrt(16 + 9))| = 2`
`implies |(10)/(5)| = 2 implies 2 = 2 `
Hence , it is a tangent of the circle .