#### Analytical Geometry Model Question Paper

11th Standard

Reg.No. :
•
•
•
•
•
•

Time : 01:00:00 Hrs
Total Marks : 50
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 kx2 + 3xy - 2y2 = 0 represent a pair of lines which are perpendicular then k is equal to

(a)

1/2

(b)

-1/2

(c)

2

(d)

-2

3. Length of the latus rectum of the parabola y2 = - 25x is

(a)

25

(b)

-5

(c)

5

(d)

-25

4. ax2 + 4xy + 2y2 = 0 represents a pair of parallel lines then 'a' is

(a)

2

(b)

-2

(c)

4

(d)

-4

5. The equation of the circle with centre (3,-4) and touches the x - axis

(a)

(x - 3)2 +(y - 4)2 = 4

(b)

(x - 3)2 +(y + 4)2 =16

(c)

(x-3)2+(y- 4)2=16

(d)

x2+y2=16

6. 5 x 2 = 10
7. Find the equation of the circle whose centre is (2,3) and which passes through (1 , 4)

8. Find the equation of the circle passing through the points (0, 1) , (4 ,3) and (1, -1)

9. Find the combined equation of the given straight lines whose separate equations are 2x+y-1= 0 and x+2y-5= 0.

10. Find the angle between the straight lines x2+4xy+y2=0

11. For what value of k does 2x2+5xy+2y2+15x+18y+k=0 represent a pair of straight lines.

12. 5 x 3 = 15
13. Show that the straight lines x + y -4 = 0, 3x + 2 = 0 and 3x -3y + 16 = 0 are concurrent

14. Find the value of 'a' for which the straight lines 3x +4y = 13; 2x -7y = -1  and ax - y -14 = 0 are concurrent

15. Find the equation of the circle passing through the points (2, 3) and (-1, 1) and whose centre is on the line x-3y-11 = 0.

16. Show that the pair of straight lines 4x2-12xy+9y2+18x-27y+8=0 represents a pair of parallel straight lines and find their separate equations.

17. For what values of a and b does the equation (a-2)x2+by2+(b-2)xy+4x+4y-1=0 represents a circle? Write down the resulting equation of the circle.

18. 4 x 5 = 20
19. Find whether the points (-1,-2), (1,0) and (-3, -4) lie above, below or on the line 3x+2y+7 =0.

20. If (4,1) is one extremity of a diameter of the circle x2 +y2 - 2x + 6y -15 = 0, find the other extremity

21. Find the equation of the parabola whose vertex is (0, 0) passing through the point (2, 3) and axis is along X-axis.

22. If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.