2023 AISS AM S3 EOY Q10
2023 AISS AM S3 EOY Q10
11 marks
Others>EOY
A tangent to a circle at the point \({(3, 1)}\) intersects the x-axis at \({x = 5}\).
- Find the equation of the tangent \({T}\).[2]
- The centre of the circle lies on the line \({y = 15 - 3x}\). Find the equation of the circle.[6]
- Find the equations of the tangents to the circle parallel to the y-axis.[3]
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Answer:(a) \(y=-\frac{1}{2}x+\frac{5}{2}\) (b) \({{(x-4)}^{2}}+{{(y-3)}^{2}}=5\)
(c) \(x=4\pm \sqrt{5}\)
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