PRACTICE PROBLEMS ON CIRCLES IN CONIC SECTIONS

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

Solution

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

Solution

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).

Solution

Problem 4 :

The radius of the circle 3x² + by² + 4bx - 6by + b² = 0

a)  1       b)  3      c)  √10       d)  √11

Solution

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)

Solution

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

Solution

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

Solution

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

Solution

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

Solution

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)

Solution

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)

Solution