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Question: For the line \(3 x + 2 y = 12\) and the circle \(x ^ { 2 } + y ^ { 2 } - 4 x - 6 y + 3 = 0\) , whi...

For the line 3x+2y=123 x + 2 y = 12 and the circle

x2+y2−4x−6y+3=0x ^ { 2 } + y ^ { 2 } - 4 x - 6 y + 3 = 0 , which of the following statements is true.

A

Line is a tangent to the circle

B

Line is a chord of the circle

C

Line is a diameter of the circle

D

None of these

Answer

Line is a diameter of the circle

Explanation

Solution

Centre of the circle is (2, 3). Obviously the line 3x+2y=123 x + 2 y = 12 passes through the centre of the circle. Hence it is a diameter of the circle.