Intersection of a Line and a Circle - Advance Quiz

Intersection of a Line and a Circle - Advance Quiz

Dear Readers,

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

Q1. A circle which passes through origin and cuts intercepts on axes a and b, the equation of circle is :

•  x^2+y^2-ax-by=0
•  x^2+y^2+ax+by=0
•  x^2+y^2-ax+by=0
•  x^2+y^2+ax-by=0

Solution
x^2+y^2-ax-by=0

Q2.Let L1 be a straight line passing through the origin and L2 be the straight line x+y=1. If the intercepts made by the circle x^2+y^2-x+3y=0 on L1 and L2 are equal, then which of the following equations can represent L1:

•  x+y=0:
•  x-y=0
•  x+7y=0
•  x-7y=0

Solution
x-y=0

Q3.  The two lines through (2, 3) from which the circle x^2+y^2=25 intercepts chords of length 8 units have equations :

•  2x+3y=13,x+5y=17
•  y=3,12x+5y=39
•  x=2,9x-11y=51
•  None of these

Solution
y=3,12x+5y=39

Q4. Circles are drawn through the point (2, 0) to cut intercepts of length 5 units on the x-axis. If their centres lie in the first quadrant, then their equation is

•  x^2+y^2-9x+2ky+14=0
•  3x^2+3y^2+27x-2ky+42=0
•  x^2+y^2-9x-2ky+14=0
•  x^2+y^2-2kx-9y+14=0

Solution
x^2+y^2-9x-2ky+14=0

Q5.A circle touches the y-axis at (0, 2) and has an intercept of 4 units on the positive side of the x-axis. Then the equation of the circle is

•  x^2+y^2-4(√2 x+y)+4=0
•  x^2+y^2-4(x+√2 y)+4=0
•  x^2+y^2-2(√2 x+y)+4=0
•  None of these

Solution
 x^2+y^2-4(√2 x+y)+4=0

Q6. Circles are drawn through the point (3, 0) to cut an intercept of length 6 units on the negative direction of the x-axis. The equation of the locus of their centres is

•  The x-axis
•  x-y=0
• The y-axis
•  x+y=0

Solution
The y-axis

Q7.Circles x^2+y^2=1 and x^2+y^2-8x+11=0 cut off equal intercepts on a line through the point (-2,1/2). The slope of the line is

•  (-1+√29)/14
•  (1+√7)/4
•  (-1-√29)/14
•  None of these

Solution
(-1+√29)/14

Q8.If 2l be the length of the intercept made by the circle x^2+y^2=a^2 on the line y=mx+c, then c^2 is equal to

•  (1+m^2)(a^2+l^2)
•  T(1+m^2)(a^2-l^2)
•  (1-m^2)(a^2+l^2)
•  (1-m^2)(a^2-l^2)

Solution
(1+m^2)(a^2-l^2)

Q9.For the circle x^2+y^2+4x-7y+12=0 the following statement is true

•  The length of tangent from (1, 2) is 7
•  Intercept on y-axis is 2
•  Intercept on x-axis is 2-√2
•  None of these

Solution
None of these

Q10. The length of the chord joining the points in which the straight line x/3+y/4=1 cuts the circle x^2+y^2=169/25 is

•  1
•  2
•  4
• 8

Solution
2