#### Analytical Geometry Important Questions

11th Standard

Reg.No. :
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Time : 02:00:00 Hrs
Total Marks : 50
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. The slope of the line 7x + 5y - 8 = 0 is

(a)

7/5

(b)

-7/5

(c)

5/7

(d)

-9/7

3. 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

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

(a)

4

(b)

5

(c)

16

(d)

25

5. The focus of the parabola x2 = 16y is

(a)

(4,0)

(b)

(-4,0)

(c)

(0,4)

(d)

(0,-4)

6. Combined equation of co-ordinate axes is

(a)

x2-y2=0

(b)

x2+y2=0

(c)

xy=c

(d)

xy=0

7. In the equation of the circle x2 +y2 = 16 then y-intercept is (are)

(a)

4

(b)

16

(c)

±4

(d)

±16

8. 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

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. 5 x 2 = 10
12. Find the equation of the circle whose centre is (-3, -2) and having circumferences 16$\pi$

13. Find the acute angle between the lines 2x - y + 3 = 0 and x + y + 2 = 0.

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

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

16. Find the parametric equations of the circle x2+y2=25

17. 5 x 3 = 15
18. Find the angle between the lines whose slopes are $\frac { 1 }{ 2 }$ and 3

19. The parabola y2 = Kx passes through the point (4, -2) find its latus rectum and focus.

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

21. Find the equation of the tangent lines to the circle x2+y2=9 which are parallel to 2x+y-3=0

22. If the equation of a circle x2+y2+ax + by = 0 passing through the points (1, 2) and (1, 1), find the values of a and b

23. 3 x 5 = 15
24. Find the value of p for which the straight lines 8px+(2-3p)y+1 = 0 and px +py -7 =0 are perpendicular to each other.

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

26. Find the equation of the parabola whose focus is (1,3) and whose directrix is x-y+2=0.