\( \DeclareMathOperator{cosec}{cosec} \)

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Here are some exam-style questions on this statement:

- "
*What is the equation of a circle, centered at the origin, that has a tangent passing through the points (-30, 0) and (0, -15)?*" ... more - "
*The diagram shows a circle with equation \(x^2+y^2=13\).*" ... more - "
*(a) Find the coordinates of the point at which the curve \(y = k^x\) intersects the y-axis.*" ... more - "
*A circle with equation \(x^2 + y^2 = 6 \) meets a one of its tangents at point \(S\).*" ... more - "
*(a) The circumference of a circle is \(16 \pi \) cm and its centre is at the origin. Find the equation of the circle.*" ... more

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