Circles Questions and answers

  1. Elementary Mathematics
    1. Area and perimeter
    2. Circles
    3. Clocks
    4. Factorisation
    5. Geometry
    6. Height and Distance
    7. Indices and Surd
    8. LCM and HCF
    9. Loci and concurrency
    10. Logarithms
    11. Polynomials
    12. Quadratic Equations
    13. Quadrilateral and parallelogram
    14. Rational expression
    15. Real Analysis
    16. Rectangular and Cartesian products
    17. Set theory
    18. Simple and Decimal fraction
    19. Simplification
    20. Statistics
    21. Straight lines
    22. Triangle
    23. Trigonometric ratio
    24. Trigonometry
    25. Volume and surface area
1). The square of the length of the tangent from \( \Large \left(3,\ -4\right) \) to the circle \( \Large x^{2}+y^{2}-4x-6y+3=0 \) is:
A). 20
B). 30
C). 40
D). 50
2). If \( \Large g^{2}+f^{2}=c \) then the equation \( \Large x^{2}+y^{2}+2gx+2fy+c=0 \) will represent:
A). a Circle of radius g
B). a circle of radius f
C). a circle of diameter \( \Large \sqrt{c} \)
D). a circle of radius 0
3). The limit of the perimeter of the regular n polygons inscribe in a circle of radius R as \( \Large n\ \rightarrow\ \infty \) is:
A). \( \Large 2 \pi R \)
B). \( \Large \pi R \)
C). \( \Large 4R \)
D). \( \Large \pi R^{2} \)
4). The value of n, for which the circle \( \Large x^{2}+y^{2}+2nx+6y+1=0 \) intersects the circle \( \Large x^{2}+y^{2}+4x+2y=0 \) orthogonally is:
A). \( \Large \frac{11}{8} \)
B). -1
C). \( \Large \frac{-5}{4} \)
D). \( \Large \frac{5}{2} \)
5). The Value of c for which the line \( \Large y=2x+c \) is a tangent to the circle \( \Large x^{2}+y^{2}=16 \) is:
A). \( \Large -16\sqrt{5} \)
B). \( \Large 4\sqrt{5} \)
C). \( \Large 16\sqrt{5} \)
D). 20


6). The radical axis of two circle and line joining their centres are:
A). Parallel
B). Perpendicular
C). Neither Parallel nor perpendicular
D). Intersecting but not perpendicular
7). Which of the following is a point on the common chord of the circles \( \Large x^{2}+y^{2}+2x-3y+6=0\ and\ x^{2}+y^{2}+x-8y-13=0 \)?
A). \( \Large \left(1,\ -2 \right) \)
B). \( \Large \left(1,\ 4\right) \)
C). \( \Large 1,\ 2 \)
D). \( \Large \left(1,\ -4\right) \)
8). The radius of the circle passing through the point \( \Large \left(6,\ 2\right) \) and two of whose diameter are \( \Large x+y=6\ and\ x+2y=4 \) is:
A). 4
B). 6
C). 20
D). \( \Large \sqrt{20} \)
9). The radius of any circle touching the lines \( \Large 3x-4y+5=0\ and\ 6x-8y-9=0 \) is:
A). 1.9
B). 0.95
C). 2.9
D). 1.45
10). The locus of the middle point of the chords of the circle \( \Large x^{2}+y^{2}=a^{2} \) such that the chords pass through a given point \( \Large \left(x_{1},\ y_{1}\right) \) is:
A). \( \Large x^{2}+y^{2}-xx_{1}-yy_{1}=0 \)
B). \( \Large x^{2}+y^{2}=x^{2}_{1}+y^{2}_{1} \)
C). \( \Large x+y=x_{1}+y'_{2} \)
D). \( \Large x+y=x^{2}_{1}+y^{2}_{1} \)
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