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 :

Solution

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

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:

Solution

x-y=0

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 :

Solution

y=3,12x+5y=39

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

Solution

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

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

Solution

x^2+y^2-4(√2 x+y)+4=0

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

Solution

The y-axis

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

Solution

(-1+√29)/14

(-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

Solution

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

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

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

Solution

None of these

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

Solution

2

2