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
31). If the circles \( \Large x^{2}+y^{2}+2x+2ky+6=0 \) and \( \Large  x^{2}+y^{2}+2ky+k=0 \) intersect orthogomally then k is:
A). \( \Large 2\ or\ -\frac{3}{2} \)
B). \( \Large -2\ or\ \frac{3}{2} \)
C). \( \Large 2\ or\ \frac{3}{2} \)
D). \( \Large -2\ or\ -\frac{3}{2} \)
32). If a > 2b > 0, then the positive value of m for which \( \Large y=mx-b\sqrt{1+m^{2}} \) is common tangent to \( \Large x^{2}+y^{2}=b^{2}\ and\ \left(x-a\right)^{2}+y^{2}=b^{2} \) is:
A). \( \Large \frac{2b}{\sqrt{a^{2}-4b^{2}}} \)
B). \( \Large \frac{\sqrt{a^{2}-4b^{2}}}{2b} \)
C). \( \Large \frac{2b}{a-2b} \)
D). \( \Large \frac{b}{a-2b} \)
33). If \( \Large \left(a\ \cos \theta _{i},\ a\ \sin \theta _{i}\right)i = 1,\ 2,\ 3 \) represent the vertices of an equilateral triangle inscribed in a circle then:
A). \( \Large \cos \theta _{1}+\cos \theta _{2}+\cos \theta _{3} = 0 \)
B). \( \Large \sec \theta _{1}+\sec \theta _{2}+\sec \theta _{3} = 0 \)
C). \( \Large \tan \theta _{1}+\tan \theta _{2}+\tan \theta _{3} = 0 \)
D). \( \Large \cot \theta _{1}+\cot \theta _{2}+\cot \theta _{3} = 0 \)
34). The distinct point \( \Large A \left(0,\ 0\right),\ B \left(0,\ 1\right),\ C \left(1,\ 0\right) and D \left(2a,\ 3a\right) \) are concylic then:
A). 'a' can attain only rational values
B). 'a' is irrational
C). cannot be concyclic for any 'a'
D). none of the above .
35). The number of rational point (S) (a point \( \Large \left(a,\ b \right) \) is called rational, if a and b both are rational number) on the circumference of a circle having centre \( \Large \left( \pi ,\ e\right) \) is:
A). at most one
B). at least two
C). exactly
D). infinite


36). If the chord of contact of tangent drawn from a point on the circle \( \Large x^{2}+y^{2}=a^{2} \) to the circle \( \Large x^{2}+y^{2}=b^{2} \) touches the circle \( \Large x^{2}+y^{2}=c^{2} \) then a, b, c are in
A). AP
B). GP
C). HP
D). none of these
37). The condition that the chord \( \Large x \cos \alpha +y \sin \alpha - p = 0 \) of \( \Large x^{2}+y^{2}-a^{2}=0 \) may subtend a right angle at the centre of circle is:
A). \( \Large a^{2} = 2p^{2} \)
B). \( \Large p^{2} = 2a^{2} \)
C). \( \Large a = 2p \)
D). \( \Large p = 2a \)
38). The equation of the circle passing through \( \Large \left(1,\ 1\right) \) and the points of intersection of \( \Large x^{2}+y^{2}+13x-3y=0 \) and \( \Large 2x^{2}+2y^{2}+4x-7y-25=0 \) is:
A). \( \Large 4x^{2}+4y^{2}-30x-10y=25 \)
B). \( \Large 4x^{2}+4y^{2}+30x-13y-25=0 \)
C). \( \Large 4x^{2}+4y^{2}-17x-10y+25=0 \)
D). none of these
39). A isoscles triangle is inscribed in the circle \( \Large x^{2}+y^{2}-6x-8y=0 \) with vertex at the origin and one of the equal side along the axis of x. Equation of the other side through the origin is:
A). \( \Large 7x-24y=0 \)
B). \( \Large 24x-7y=0 \)
C). \( \Large 7x+24y=0 \)
D). \( \Large 24x+7y=0 \)
40). If the lines \( \Large 3x-4y-7=0\ and\ 2x-3y-5=0 \) are two diameters of a circle of area \( \Large 49 \pi \) sq unit, the equation of the circle is:
A). \( \Large x^{2}+y^{2}+2x-2y-62=0 \)
B). \( \Large x^{2}+y^{2}-2x+2y-62=0 \)
C). \( \Large x^{2}+y^{2}-2x+2y-47=0 \)
D). \( \Large x^{2}+y^{2}+2x-2y-47=0 \)
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