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

**Q1.**y=mx+c is a chord of a circle of radius a and the diameter of the circle lies along x-axis and one end of this chord is origin. The equation of the circle described on this chord as diameter is :

Solution

(1+m^2)(x^2+y^2)-2a(x+my)=0

(1+m^2)(x^2+y^2)-2a(x+my)=0

**Q2.**If y=2x is a chord of the circle x^2+y^2-10x=0, then the equation of the circle of which this chord is a diameter, is :

Solution

x^2+y^2-2x-4y=0

x^2+y^2-2x-4y=0

**Q3.**The circle on the chord x cosÎ±+y sinÎ±=p of the circle x^2+y^2=a^2 as diameter has the equation:

Solution

x^2+y^2-a^2-2p(x cosÎ±+y sinÎ±-p)=0

x^2+y^2-a^2-2p(x cosÎ±+y sinÎ±-p)=0

**Q4.**The equation of circle which touches the axes of coordinates and the line x/3+y/4=1 and whose centre lies in the first quadrant is x^2+y^2-2cx-2cy+c^2=0, where c is

Solution

6

6

**Q5.**The equation of a circle which touches both axes and the line 3x-4y+8=0 and lies in the third quadrant is

Solution

x^2+y^2+4x+4y+4=0

x^2+y^2+4x+4y+4=0

**Q6.**Equation of the circle which touches the lines x=0,y=0 and 3x+4y=4 is

Solution

6a^2

6a^2

**Q7.**The equation of the circumcircle of the triangle formed by the lines y+√3 x=6,y-√3 x=6 and y = 0, is

Solution

x^2+y^2=25

x^2+y^2=25

**Q8.**A variable circle passes through the fixed point A(p,q) and touches x-axis. The locus of the other end of the diameter through A is

Solution

(x-p)^2=4qy

(x-p)^2=4qy

**Q9.**If a circle passes through the points of intersection of the coordinate axes with the lines Î»x-y+1=0 and x-2y+3=0, then the value of is

Solution

2

2

**Q10.**Equation to the circles which touch the lines 3x-4y+1=0,4x+3y-7=0 and pass through (2, 3) are

Solution

Both (a) and (b)

Both (a) and (b)