The number of common tangents to the two circles x2 + y - 8x + 2y = 0 and x2 + y2 - 2x - 16y + 25 = 0 is :
1
2
3
4
Observe the following statements :
I. The circle x2 + y2 - 6x - 4y - 7 = 0 touches y-axis.
II. The circle x2 + y2 + 6x + 4y - 7 = 0 touches
x-axis. Which of the following is a correct statement ?
Both I and II are true
Neither I nor II is true
I is true, II is false
I is false, II is true
The equation of the circle of radius 3 that lies in the fourth quadrant and touching the lines x = 0 and y = 0 is
x2 + y2 - 6x + 6y + 9 = 0
x2 + y2 - 6x - 6y + 9 = 0
x2 + y2 + 6x - 6y + 9 = 0
x2 + y2 + 6x + 6y + 9 = 0
The inverse point of (1, 2) with respect to the circle
x2 + y2 - 4x - 6y + 9 = 0 is
(0, 0)
(1, 0)
(0, 1)
(1, 1)
For the parabola y2 + 6y - 2x + 5 = 0
(I) The vertex is (- 2, - 3)
(II) The directrix is y + 3 = 0
Which of the following is correct ?
Both I and II are true
I is true, II is false
I is false, II is true
Both I and II are false
The value of k, If (1, 2), (k, - 1) are conjugate points with respect to the ellipse 2x2 + 3y2 = 6 is
2
4
6
8
If the lines 2x - 3y = 5 and 3x - 4y = 7 are two diameters of a circle of radius 7, then the equation of the circle is
x2 + y2 + 2x - 4y - 47 = 0
x2 + y2 = 49
x2 + y2 - 2x + 2y - 47 = 0
x2 + y2 = 17