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Definition, Equation of the Circle - Basic Quiz

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

Q1. The two points A and B in a plane such that for all points P lies on circle satisfied PA/PB = k then k will not be equal to :
•  0
•  1
•  2
•  None of these
Solution
1

Q2.Locus of a point which moves such that sum of the squares of its distances from the sides of a square of side unity is 9, is :
•  Straight line
•  Circle
•  Parabola
•  None of these
Solution
Circle

Q3.  The equation of the circle which touches both the axes and whose radius is a, is :
•   x^2+y^2-2ax-2ay+a^2=0
•  x^2+y^2+ax+ay-a^2=0
•  x^2+y^2+2ax+2ay-a^2=0
•  x^2+y^2-ax-ay+a^2=0
Solution
x^2+y^2-2ax-2ay+a^2=0

Q4. ABCD is a square the length of whose side is a. Taking AB and AD as the coordinate axes, the equation of the circle passing through the vertices of the square, is
•  x^2+y^2+ax+ay=0
•  x^2+y^2-ax-ay=0
•  x^2+y^2+2ax+2ay=0
•  x^2+y^2-2ax-2ay=0
Solution
x^2+y^2-ax-ay=0

Q5.The equation of the circle in the first quadrant touching each coordinate axis at a distance of one unit from the origin is
•  x^2+y^2-2x-2y+1=0
•  x^2+y^2-2x-2y-1=0
•  x^2+y^2-2x-2y=0
•  None of these
Solution
x^2+y^2-2x-2y+1=0

Q6. The equation of the circle which touches both axes and whose centre is , is
•  x^2+y^2+2x_1 (x+y)+x_1^2=0
•  x^2+y^2-2x_1 (x+y)+x_1^2=0
• x^2+y^2=x_1^2+y_1^2
•  x^2+y^2+2xx_1+2yy_1=0
Solution
x^2+y^2-2x_1 (x+y)+x_1^2=0

Q7.The equation of the circle which touches x-axis and whose centre is (1, 2), is
•  x^2+y^2-2x+4y+1=0
•  x^2+y^2-2x-4y+1=0
•  x^2+y^2+2x+4y+1=0
•  x^2+y^2+4x+2y+4=0
Solution
x^2+y^2-2x-4y+1=0

Q8.The equation of the circle having centre (1, – 2) and passing through the point of intersection of lines 3x+y=14,2x+5y=18 is
•  x^2+y^2-2x+4y-20=0
•  Tx^2+y^2-2x-4y-20=0
•  x^2+y^2+2x-4y-20=0
•  x^2+y^2+2x+4y-20=0
Solution
x^2+y^2-2x+4y-20=0

Q9.The equation of the circle passing through (4, 5) and having the centre at (2, 2), is
•  x^2+y^2+4x+4y-5=0
•  x^2+y^2+hx+ky=0
•  x^2+y^2-4x=13
•  x^2+y^2-4x-4y+5=0
Solution
x^2+y^2+hx+ky=0

Q10. The equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line is
•  x^2+y^2+4x-10y+25=0
•  x^2+y^2-4x-10y+25=0
•  x^2+y^2-4x-10y+16=0
• x^2+y^2-4x-10y+16=0
Solution
x^2+y^2-4x-10y+25=0

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