JEE Main & Advanced Mathematics Circle and System of Circles Question Bank

done Numerical Value Type Questions - Circle Total Questions - 15

• question_answer1)
  Find the area of square inscribed in a circle \[{{x}^{2}}+{{y}^{2}}-6x-8y=0\].
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• question_answer2)
  If the circumference of the circle \[{{x}^{2}}+{{y}^{2}}+8x+8y-b=0\] is bisected by the circle \[{{x}^{2}}+{{y}^{2}}-2x+4y+a=0\] then find \[a+b\].
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• question_answer3)
  Tangents are drawn from point (4, 5) to the circle\[{{x}^{2}}+{{y}^{2}}-4x-2y-11=0\]. Find the area of the quadrilateral formed by these tangents and radii joining their point of contacts.
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• question_answer4)
  Find the sum of square of the length of the chords intercepted by the line \[x+y=n\,\,;\,\,n\,\,\in \,\,N\] on the circle \[{{x}^{2}}+{{y}^{2}}=4\].
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• question_answer5)
  Two circle of equal radius r cut orthogonally. If their centres are (2, 3) and (5, 6) then find value of r.
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• question_answer6)
  Find the number of common tangent(s) to the circles \[~{{x}^{2}}+{{y}^{2}}+2x+8y-23=0\] and \[{{x}^{2}}+{{y}^{2}}-4x-\text{1}0y+19=0\].
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• question_answer7)
  If the circle \[{{x}^{2}}+{{y}^{2}}+4x+22y+c=0\] bisects the circumference of the circle \[{{x}^{2}}+{{y}^{2}}-2x+8y-d=0,\] then find \[c+d.\]
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• question_answer8)
  Find the greatest distance of the point \[P\text{ }(10,\,\,7)\] from the circle \[{{x}^{2}}+{{y}^{2}}-4x-2y-20=0\].
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• question_answer9)
  If the tangent at the point P on the circle \[{{x}^{2}}+{{y}^{2}}+6x+6y=2\] meets the straight line \[5x-2y+6=0\]at a point Q on the y-axis, then find the length of PQ.
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• question_answer10)
  If the length of the common chord of the circles \[{{x}^{2}}+{{y}^{2}}+2x+3y+1=0\] and \[{{x}^{2}}+{{y}^{2}}+4x+3y+2=0\] is \[\frac{k}{\sqrt{2}}\] then find k.
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• question_answer11)
  Find maximum number of circles possible touching both axes and line \[3x+4y=12.\]
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• question_answer12)
  If the radius of the circle passing through the point (6, 2), two of whose diameters are \[x+y=6\] and \[x+2y=4\] is \[k\sqrt{5}\] then find k.
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• question_answer13)
  If the equation \[\lambda {{x}^{2}}+\left( 2\lambda -3 \right){{y}^{2}}-4x-1=0\] represents a circle whose radius is \[\frac{\sqrt{7}}{k}\] then find k.
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• question_answer14)
  If (-3,2) lies on the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] which is concentric with the circle \[{{x}^{2}}+{{y}^{2}}+6x+8y-5=0,\]then find value of c.
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• question_answer15)
  If the line \[y=7x-25\] meets the circle \[{{x}^{2}}+{{y}^{2}}=25\] in the points A, B, and the distance between A and B is \[k\sqrt{2}\] then find k.  
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