#### Analytical Geometry - Important Question Paper

11th Standard

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Time : 01:00:00 Hrs
Total Marks : 50

Part A

10 x 1 = 10
1. The angle between the pair of straight lines x2 - 7xy + 4y2 = 0 _______.

(a)

$tan^{-1}\left(1\over 3\right)$

(b)

$tan^{-1}\left(1\over 2\right)$

(c)

$tan^{-1}\left(\sqrt{33}\over 5\right)$

(d)

$tan^{-1}\left(5\over\sqrt{33}\right)$

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 x-intercept of the straight line 3x + 2y - 1 = 0 is _______.

(a)

3

(b)

2

(c)

1/3

(d)

1/2

4. If the centre of the circle is (-a, -b) and radius is $\sqrt{a^2-b^2}$, then the equation of circle is _______.

(a)

x2+y2+2ax+2by+2b2=0

(b)

x2+y2+2ax +2by-2b2=0

(c)

x2 +y2 - 2ax - 2by - 2b2 = 0

(d)

x2 + y - 2ax - 2by + 2b2 = 0

5. Combined equation of co-ordinate axes is _______.

(a)

x2-y2=0

(b)

x2+y2=0

(c)

xy=c

(d)

xy=0

6. If the perimeter of the circle is 8π units and centre is (2,2) then the equation of the circle is _______.

(a)

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

(b)

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

(c)

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

(d)

x2 + y2 =4

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

(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

8. If the circle touches x axis, y axis and the line x = 6 then the length of the diameter of the circle is _______.

(a)

6

(b)

3

(c)

12

(d)

4

9. The eccentricity of the parabola is _______.

(a)

3

(b)

2

(c)

0

(d)

1

10. The distance between directrix and focus of a parabola y2 = 4ax is _______.

(a)

a

(b)

2a

(c)

4a

(d)

3a

11. Part B

6 x 2 = 12
12. If A (-1,1) and B (2,3) are two fixed points, then find the locus of a point P So that the area of triangle APB = 8 Sq.units

13. Find the equation of the following circles having the centre (3,5) and radius 5 units

14. Find the equation of the following circles having the centre (0,0) and radius 2 units

15. Find the center and radius of the circle  x2 + y2 - 22x - 4y + 25 = 0

16. Find the center and radius of the circle 5x2 + 5y2 + 4x - 8y - 16 = 0

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

18. Part C

6 x 3 = 18
19. Find the equation of the parabola whose focus is (-3, 2) and the directrix is x + y = 4.

20. A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16, find its locus.

21. Prove that the lines (b - c) x + (c - a) y + (a - b) = 0, (c - a) x + (a - b) y + (b - c) = 0, and (a - b) x + (b - c) y+c-a=0 are concurrent.

22. Find the slope of the lines which make an angle of 45° with the line 3x - y + 5 = 0.

23. Find the combined equation of the straight line through the origin, one of which is parallel to and the other is perpendicular to the straight line 2x + y + 1 = 0

24. Find the equation of the circle having centre at (3, -4) and touching the line 5x + 12y - 12 = 0

25. Part D

2 x 5 = 10
26. Show that the pair of straight lines 4x2 +12xy + 9y2 -6x -9y +2 = 0 represents two parallel straight lines and also find the separate equations of the straight lines..

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