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The number of common tangents to two circles ${{x}^{2}}+{{y}^{2}}=4$ and ${{x}^{2}}-{{y}^{2}}-8x+12=0$ is
If $2x-4y=9$ and $6x-12y+7=0$ are the tangents of same circle, then its radius will be
The tangent at P, any point on the circle ${{x}^{2}}+{{y}^{2}}=4$ , meets the coordinate axes in A and B, then
The number of common tangents to the circles ${{x}^{2}}+{{y}^{2}}-x=0,\,{{x}^{2}}+{{y}^{2}}+x=0$ is
The equation of tangent to the circle ${{x}^{2}}+{{y}^{2}}={{a}^{2}}$ parallel to$y=mx+c$ is
If the circle ${{(x-h)}^{2}}+{{(y-k)}^{2}}={{r}^{2}}$ touches the curve $y={{x}^{2}}+1$ at a point (1, 2), then the possible locations of the points (h, k) are given by
The line $ax+by+c=0$ is a normal to the circle ${{x}^{2}}+{{y}^{2}}={{r}^{2}}$ . The portion of the line $ax+by+c=0$ intercepted by this circle is of length
$x=7$ touches the circle ${{x}^{2}}+{{y}^{2}}-4x-6y-12=0$ , then the coordinates of the point of contact are
If $a>2b>0$ then the positive value of m for which $y=mx-b\sqrt{1+{{m}^{2}}}$ is a common tangent to ${{x}^{2}}+{{y}^{2}}={{b}^{2}}$ and ${{(x-a)}^{2}}+{{y}^{2}}={{b}^{2}}$ , is
The circles ${{x}^{2}}+{{y}^{2}}=9$ and ${{x}^{2}}+{{y}^{2}}-12y+27=0$ touch each other. The equation of their common tangent is

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