Definition, Equation of the Circle-Advance

Definition, Equation of the Circle - Advance Quiz

Dear Readers,

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 :

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

Solution
(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 :

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

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

Q3.  The circle on the chord x cos⁡α+y sin⁡α=p of the circle x^2+y^2=a^2 as diameter has the equation:

•  x^2+y^2-a^2-2p(x cos⁡α+y sin⁡α-p)=0
•  x^2+y^2+a^2+2p(x cos⁡α-y sin⁡α+p)=0
•  x^2+y^2-a^2+2p(x cos⁡α+y sin⁡α+p)=0
•  x^2+y^2-a^2-2p(x cos⁡α-y sin⁡α-p)=0

Solution
x^2+y^2-a^2-2p(x cos⁡α+y sin⁡α-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

•  1
•  2
•  3
•  6

Solution
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

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

Solution
 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

•  x^2-4x+y^2+4y+4=0
•  6a^2
• r(< a)
•  x^2+4x+y^2-4y+4=0

Solution
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

•  x^2+y^2-4y=0
•  x^2+y^2+4x=0
•  x^2+y^2=25
•  x^2+y^2+4x=12

Solution
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

•  (y-q)^2=4px
•  T(x-q)^2=4py
•  2x^2+2y^2-3x=0
•  (x-p)^2=4qy

Solution
(x-p)^2=4qy

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

•  1
•  2
•  3
•  4

Solution
2

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

•  (x-2)^2+(y-8)^2=25
•  5x^2+5y^2-12x-24y+31=0
•  Both (a) and (b)
• None of these

Solution
Both (a) and (b)