Problem 1 :
The equation of the circle passing through (1, 5) and (4, 1) and touching y-axis is
x2 + y2 - 5x - 6y + 9 +λ(4x+3y-19) = 0
where λ is equal to
a) 0, -40/9 b) 0 3) 40/9 d) -40/9
Problem 2 :
The circle x2 + y2 = 4x + 8y + 5 intersects the line 3x - 4y = m at two distinct points if
a) 15 < m < 65 b) 35 < m < 85
3) -85 < m < -35 d) -35 < m < 15
Problem 3 :
The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3).
Problem 4 :
The radius of the circle 3x2 + by2 + 4bx - 6by + b2 = 0
a) 1 b) 3 c) √10 d) √11
Problem 5 :
The center of the circle inscribed in a square formed by the lines x2 - 8x + 12 = 0 and y2 - 14y + 45 = 0 is
a) (4, 7) b) (7, 4) c) (9, 4) d) (4, 9)
Problem 6 :
The equation of the normal to the circle x2 + y2 - 2x - 2y + 1 = 0 which is parallel to the line 2x + 4y = 3 is
a) x + 2y = 3 b) x + 2y + 3 = 0
c) 2x + 4y + 3 = 0 d) x - 2y + 3 = 0
Problem 7 :
The radius of the circle is passing through the point (6, 2) two of whose diameters are x + y = 6 and x + 2y = 4 is
a) 10 b) 2√5 c) 6 d) 4
Problem 8 :
The equation of the circle passing through the foci of the ellipse
having center at (0, 3) is
a) x2 + y2 - 6y - 7 = 0 b) x2 + y2 - 6y + 7 = 0
c) x2 + y2 - 6y - 5 = 0 d) x2 + y2 - 6y + 5 = 0
Problem 9 :
Let C be the circle with center at (1, 1) and radius = 1. If T is the circle centered at (0, y) passing through the origin and touching the circle C externally, then the radius of T is equal to
a) √3/√2 b) √3/2 c) 1/2 d) 1/4
Problem 10 :
If the coordinates at one end of a diameter of the circle
x2 + y2 - 8x - 4y + c = 0
are (11, 2) the coordinates of the other end are
a) (-5, 2) b) (-3, 2) c) (5, -2) d) (-2, 5)
Problem 11 :
The circle passing through (1, -2) and touching the axis of x at (3, 0) passing through the point
a) (-5, 2) b) (2, -5) c) (5, -2) d) (-2, 5)
1) λ = 0 and λ = -40/9, option a
2) -35 < m < 15, option d
3) k = 5/3, option b
4) √10
5) center of the circle is (4, 7), option a
6) x + 2y = 3
7) r = 2√5
8) x2 + y2 - 6y - 7 = 0
9) 1/4.
10) (-3, 2).
11) (5, -2)
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