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Intersection of a Line and a Circle - Basic Quiz

Mathematics is an important subject in SSC,DSSB & Other Exams. .

Q1. A circle touches the y-axis at the point (0, 4) and cuts the x-axis in a chord of length 6 units. The radius of the circle is :
•  3
•  4
•  5
•  6
Solution
5

Q2.The radius of a circle which touches y-axis at (0, 3) and cuts intercept of 8 units with x-axis, is :
•  3:
•  2
•  5
•  8
Solution
5

Q3.  The intercept on the line y=x by the circle x^2+y^2-2x=0 is AB. Equation of the circle with AB as a diameter is :
•  x^2+y^2-x-y=0
•  x^2+y^2-2x-y=0
•  x^2+y^2-x+y=0
•  x^2+y^2+x-y=0
Solution
x^2+y^2-x-y=0

Q4. The circle x^2+y^2-3x-4y+2=0 cuts x-axis at
•  (2, 0), (– 3, 0)
•  (3, 0), (4, 0)
•  (1, 0), (– 1, 0)
•  (1, 0), (2, 0)
Solution
(1, 0), (2, 0)

Q5.If the line y=x+3 meets the circle x^2+y^2-8x-4=0 at A and B, then the equation of the circle having AB as a diameter will be
•  x^2+y^2+3x-3y-a^2+9=0
•  x^2+y^2-3x+3y-a^2+9=0
•  x^2+y^2+3x+3y-a^2+9=0
•  None of these
Solution
x^2+y^2+3x-3y-a^2+9=0

Q6. If the circle x^2+y^2+2ax+8y+16=0 touches x-axis, then the value of a is
•  +-16
•  +-4
• +-8
•  +-1
Solution
+-4

Q7.The length of the intercept made by the circle x^2+y^2=1 on the line x+y=1 is
•  2
•  √2
•  x^2+y^2=5
•  2√2
Solution
√2

Q8.The AM of the abscissae of points of intersection of the circle x^2+y^2+2gx+2fy+c=0 with x-axis is
•  g
•  T-g
•  f
•  -f
Solution
-g

Q9.The straight line (x-2)+(y+3)=0 cuts the circle (x-2)^2+(y-3)^2=11 at
•  No points
•  One point
•  Two points
•  None of these
Solution
No points

Q10. The equation of a circle whose centre is (3, – 1) and which cuts off a chord of length 6 on the line 2x-5y+18=0
•  (x-3)^2+(y+1)^2=38
•  (x+3)^2+(y-1)^2=38
•  (x-3)^2+(y+1)^2=√38
• None of these
Solution
(x-3)^2+(y+1)^2=38

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