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
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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