prove that the circle x² +y²-6x-2y+9=0 touches the x-axis
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Step-by-step explanation:
given equation of circle
x² + y² - 6x - 2y + 9 = 0
to prove that the circle touches x axis
put y = 0 in the given equation
x² + 0² - 6x - 2*0 + 9 = 0
=> x² - 6x + 9 = 0
=> x² - 3x - 3x + 9 = 0
=> x(x - 3) - 3(x - 3) = 0
=> (x - 3)² = 0
=> x = 3
therefore the given circle touches the x axis at
x = 3
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