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Circle and System of Circles Test - 30

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Circle and System of Circles Test - 30
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    The radius of a circle which touches y-axis at (0, 3) andcuts intercept of 8 units with x-axis, is
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    Apoint P moves in such a way that the ratio of its distance from two coplanar points is always a fixed number (≠1). The its locus is
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    Locus of the centre of the circle touching both the co-ordinates axis is
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    A line meets the coordinate axes in A and B. A circle is circumscribed about the triangle OAB. If m and n are the distance of the tangents to the circle at the points A and B respectively from the origin, the diameter of the circle is
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