Circles Questions and answers

  1. Elementary Mathematics
    1. Quadratic Equations
    2. Simplification
    3. Area and perimeter
    4. Volume and surface area
    5. Geometry
    6. Trigonometry
    7. Polynomials
    8. Height and Distance
    9. Simple and Decimal fraction
    10. Indices and Surd
    11. Logarithms
    12. Trigonometric ratio
    13. Straight lines
    14. Triangle
    15. Circles
    16. Quadrilateral and parallelogram
    17. Loci and concurrency
    18. Statistics
    19. Rectangular and Cartesian products
    20. Rational expression
    21. Set theory
    22. Factorisation
    23. LCM and HCF
    24. Clocks
    25. Real Analysis
11). The equations of the tangents to the circle \( \Large x^{2}+y^{2}-6x+4y-12=0 \) which are parallel to the line \( \Large 4x+3y+5=0 \),are
A). \( \Large 4x+3y+11=0 \) and \( \Large 4x+3y+8=0 \)
B). \( \Large 4x+3y-9=0 \) and \( \Large 4x+3y+7=0 \)
C). \( \Large 4x+3y+19=0 \) and \( \Large 4x+3y-31=0 \)
D). \( \Large 4x+3y-10=0 \) and \( \Large 4x+3y+12=0 \)
12). The lines \( \Large 2x-3y=5\ and\ 3x-4y=7 \) are diameters of a circle having area as 154 sq unit. Then the equation of the circle is:
A). \( \Large x^{2}+y^{2}+2x-2y=62 \)
B). \( \Large x^{2}+y^{2}+2x-2y=47 \)
C). \( \Large x^{2}+y^{2}-2x+2y=47 \)
D). \( \Large x^{2}+y^{2}-2x+2y=62 \)
13). The pole of the straight line \( \Large x+2y=1 \) with respect to the circle \( \Large x^{2}+y^{2}=5 \) is:
A). \( \Large \left(5,\ 5\right) \)
B). \( \Large \left(5,\ 10\right) \)
C). \( \Large \left(10,\ 5\right) \)
D). \( \Large \left(10,\ 10\right) \)
14). If the circle \( \Large x^{2}+y^{2}+6x-2y+k=0 \) bisects the circumference of the circle \( \Large x^{2}+y^{2}+2x-6y-15=0 \) then k is equal to:
A). 21
B). -21
C). 23
D). -23
15). If \( \Large 5x-12y=10 \) and \( \Large 12y-5x+16=0 \) are two tangents to a circle, then the radius of the circle is
A). 1
B). 2
C). 4
D). 6


16). Equation of the circle passing through the point \( \Large \left(3,\ 4\right) \) and concentric with the circle \( \Large x^{2}+y^{2}-2x-4y+1=0 \) is
A). \( \Large x^{2}+y^{2}-2x-4y=0 \)
B). \( \Large x^{2}+y^{2}-2x-4y+3=0 \)
C). \( \Large x^{2}+y^{2}-2x-4y-3=0 \)
D). none of the above
17). Circle \( \Large x^{2}+y^{2}-2x-nx-1=0 \) passes through two fixed points, co-ordinates of the points are
A). \( \Large \left(0,\ \pm 1\right) \)
B). \( \Large \left(\pm\ 1,\ 0\right) \)
C). \( \Large \left(0,\ 1\right)\ and\ \left(0,\ 2\right) \)
D). \( \Large \left(0,\ -1\right)\ and\ \left(0,\ -2\right) \)
18). Centre of circle whose normals are \( \Large x^{2}-2xy-3x+6y=0 \) is
A). \( \Large \left(3,\ \frac{3}{2}\right) \)
B). \( \Large \left(3,\ -\frac{3}{2}\right) \)
C). \( \Large \left(\frac{3}{2},\ 3\right) \)
D). none of these
19). The locus of centre of a circle \( \Large x^{2}+y^{2}-2x-2y+1=0 \) which rolls outside the circle \( \Large x^{2}+y^{2}-6x+8y=0 \) is:
A). \( \Large x^{2}+y^{2}-2x-2y-34=0 \)
B). \( \Large x^{2}+y^{2}-6x+8y+11=0 \)
C). \( \Large x^{2}+y^{2}-6x+8y-11=0 \)
D). none of these
20). A line through \( \Large P \left(1,\ 4\right) \) intersect a circle \( \Large x^{2}+y^{2}=16 \) at A and B, then PA-PB is equal to:
A). 1
B). 2
C). 3
D). 4
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