Centre and Radius of a Circle - Advance Quiz

Centre and Radius of a Circle - Advance Quiz

Dear Readers,

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

Q1. If 2x-4y=9 and 6x-12y+7=0 are the tangents of same circle, then its radius will be :

•   √3/5
•  17/(6√5)
•  (2√5)/3
•  17/(3√5)

Solution
17/(6√5)

Q2.If 5x-12y+10=0 and 12y-5x+16=0 are two tangents to a circle, then the radius of the circle is :

•  1:
•  2
•  4
•  6

Solution
1

Q3.  If x-y=0. is the equation of a circle then its radius is :

•  3√2
•  2√3
•  2√2
•  None of these

Solution
None of these

Q4. 93. C1 is a circle of radius 1 touching the x-axis and the y-axis. C2 is another circle of radius >1 and touching the axes as well as the circle C1. Then the radius of C2 is

•  3-2√2
•  3+2√2
•  3+2√3
•  None of these

Solution
3+2√2

Q5.If p and q be the longest distance and the shortest distance respectively of the point (– 7, 2) from any point (, ) on the curve whose equation is x^2+y^2-10x-14y-51=0 then GM of p and q is equal to

•  2√11
•  5√5
•  13
•  None of these

Solution
 2√11

Q6. The equation of a circle is x^2+y^2=4. The centre of the smallest circle touching this circle and the line x+y=5√2 has the coordinates

•  (7/(2√2),7/(2√2))
•  (3/2,3/2)
• (-7/(2√2),-7/(2√2))
•  None of these

Solution
(7/(2√2),7/(2√2))

Q7. A circle touches the line 2x-y-1=0 at the point (3, 5). If its centre lies on the line x+y=5 then the centre of that circle is

•  (3, 2)
•  (– 3, 8)
•  (4, 1)
•  (8, – 3)

Solution
(– 3, 8)

Q8.The locus of the centre of the circle (x cos⁡θ+y sin⁡θ-a)^2+(x sin⁡θ-y cos⁡θ+a)^2=a^2 is

•  x^2+y^2=a^2
•  Tx^2+y^2=2a^2
•  x^2+y^2=4a^2
•  x^2+y^2-2ax-2ay+a^2=0

Solution
x^2+y^2=2a^2

Q9.If a circle S(x,y)=0 touches at the point (2, 3) of the line x+y=5 and S(1,2)=0, then radius of such circle

•  2
•  4
•  1/2
•  1/√2

Solution
1/√2

Q10. If one end of a diameter of the circle x^2+y^2-4x-6y+11=0 be (3, 4), then the other end is

•  (0, 0)
•  (1, 1)
•  (1, 2)
• (2, 1)

Solution
(1, 2)