#### Analytical Geometry Book Back Questions

11th Standard

Reg.No. :
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Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
1. If m1 and m2 are the slopes of the pair of lines given by ax2+ 2hxy + by2 = 0, then the value of m1 + m2 is

(a)

2h/b

(b)

-2h/b

(c)

2h/a

(d)

-2h/a

2. If the lines 2x - 3y - 5 = 0 and 3x - 4y - 7 = 0 are the diameters of a circle, then its centre is

(a)

(-1, 1)

(b)

(1,1)

(c)

(1, -1 )

(d)

(-1, -1)

3. The locus of the point P which moves such that P is always at equidistance from the line x + 2y+ 7 = 0 is

(a)

x+2y+2=0

(b)

x - 2y + 1 = 0

(c)

2x - y + 2 = 0

(d)

3x + y + 1=0

4. (1, - 2) is the centre of the circle x2 + y2 + ax + by - 4 = 0 , then its radius

(a)

3

(b)

2

(c)

4

(d)

1

5. The length of the tangent from (4,5) to the  circle x2 +y2 = 16 is

(a)

4

(b)

5

(c)

16

(d)

25

6. 5 x 2 = 10
7. Find the centre and radius of the circle x2 + y2 = 16

8. If the lines x+ y = 6 and x + 2y = 4 are diameters of the circle , and the circle passes through the point (2,6)  then find its equation.

9. Find the angle between the pair of lines represented by the equation 3x2+10xy+8y2+14x+22y+15=0.

10. Find the focus, equation of the directrix, vertrix and length of latus sections of the parabola x2=6y.

11. If the centre of the circle x2+y2+2x-6y+1=0 lies on a straight line ax+2y+2=0, then find the value of ‘a’

12. 3 x 5 = 15
13. Find the angle between the pair of straight lines 3x2 -5xy -2y2 +17x + y + 10 = 0

14. Find whether the points (-1,-2), (1,0) and (-3, -4) lie above, below or on the line 3x+2y+7 =0.

15. Show that the equation 2x2+7xy+3y2+5x+5y+2=0 represent two straight lines and find their separate equations.