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Circles Test - 3

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Circles Test - 3
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Weekly Quiz Competition
  • Question 1
    1 / -0
    The locus of the centre of a circle which cuts off intercepts of length 2a and 2b from x-axis and y-axis respectively, is
  • Question 2
    1 / -0

    Two perpendicular tangents to the circle x2+y2=r2 meet at P. The locus of P is


    Solution

    locus of P is a circle with centre at origin and radius √2r2.This is known as the director circle of the circle x2+y2=r2

  • Question 3
    1 / -0
    In the given figure, AB is the diameter of the largest circle, P and Q are centres of the two small circles touching the largest circle at points A and B, respectively. The small circles touch each other externally at point M. What is the radius of the small circle with centre Q?

  • Question 4
    1 / -0

    If (x-a)2 + (y-b)2 = c2 represents a circle, then

    Solution

    (x-a)2 + (y-b)2 = c2  here (a,b) is center and c is the radius


    and radius cannot be zero because if radius is zero it will become a point or degenerate circle so c≠0.

  • Question 5
    1 / -0
    The area of the circle in which a chord of length √2 makes an angle π/2 at the centre is
  • Question 6
    1 / -0

    Circumcentre of the triangle, whose vertices are (0, 0), (6, 0) and (0, 4) is

    Solution

    circumcentre of a right angled triangle ABC right angled at A is b+c/2 as circumcentre of right angled triangle lies on the mid pont of the hypotenuse.

    so mid point of BC=(6+0/2,0+4/2) i.e.(3,2)

  • Question 7
    1 / -0
    The director circle is the locus of the point of intersection of
  • Question 8
    1 / -0
    The area of the circle with centre at (1, 2) and passing through (4, 6) is
  • Question 9
    1 / -0
    The circles whose equations are x2 + y2 + c2 = 2ax, and x2 + y2 + c2 – 2by = 0 will touch each other externally if
  • Question 10
    1 / -0
    What will be the locus of point whose distance from the point (–g, –f) is always 'a'? (Given k = g2 + f2 – a2)
  • Question 11
    1 / -0
    x = a cos t, y = a sin t is the parametric form of a/an 
  • Question 12
    1 / -0
    O is the centre of the given circle and PR is the diameter. AT is the tangent to the circle at point A. What is the measure of PQR?

  • Question 13
    1 / -0
    A circle passes through the origin and cuts intercepts a and b on the axes. The equation of the circle is 
  • Question 14
    1 / -0
    The area of a circle with centre (h, k) and radius a is
  • Question 15
    1 / -0
    If the centre of a circle is (2, 3) and a tangent to the circle is x + y = 1, then the equation of this circle is
  • Question 16
    1 / -0
    Find the center and the radius of the circle (x + 5)2 + (y + 7)2 = 36.
  • Question 17
    1 / -0
    The equation of a circle with centre (4, 3) and touching the circle x2 + y2 = 1, is
  • Question 18
    1 / -0
    A circle is inscribed in an equilateral triangle of side a. The area of any square inscribed in the circle is
  • Question 19
    1 / -0

    The length of the chord joining the point ( 4 cos θ, 4 sin θ) and 4 ( cos(θ+60o), 4 sin(θ + 60o)) of the circle x2+y2=16 is

    Solution

  • Question 20
    1 / -0
    Let C be any circle with centre (0, ). How many rational points are there on C?
  • Question 21
    1 / -0

    The number of tangents to the circle x2+y2−8x−6y+9=0, which pass through the point ( 3, - 2), is

    Solution

    x2+y2−8x−6y+9=0 


    After completing the square,we get


    (x−4)2+(y−3)2=(4)2

    so center is (4,3) and radius is 4.

    Distance between center and given point √(4−3)2+(3+2)2=√26 which is greater than 4.

    hence point lies outside the circle .

    Since point lies outside of the circle there will be 2 tangents since two tangents can be drawn from external point to a circle.

  • Question 22
    1 / -0
    The number of tangents which can be drawn from the point (– 1, 2) to the circle x2 + y2 + 2x – 4y + 4 = 0 is
  • Question 23
    1 / -0
    In the given figure, O is the centre of the circle and PQ is a tangent to the circle at P.



    If OP = 3 cm and PQ = 12 cm, then what is the length of OQ?
  • Question 24
    1 / -0

    The value of k, such that the equation  2x2+2y2−6x+8y+k=0 represents a point circle, is

    Solution

  • Question 25
    1 / -0
    Which of the following statements is true for the two circles x2 + y2 – 4y = 0 and x2 + y2 – 8y = 0?
  • Question 26
    1 / -0
    If the equation x2 + 2gx + 2fy + c = 0 represents a circle with x-axis as a diameter and radius a, then
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