#### Analytical Geometry Important Questions

11th Standard

Reg.No. :
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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. 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)

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

3. 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)

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

(a)

a

(b)

2a

(c)

4a

(d)

3a

5. The equation of directrix of the parabola y2 = - x is

(a)

4x+ 1 =0

(b)

4x - 1 = 0

(c)

x - 4=0

(d)

x + 4 = 0

6. 5 x 2 = 10
7. Find the equation of the following circles having the center (3,5) and radius 5 units

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

9. Find the centre and radius of the circle x2 + y2 = 16

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

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

12. 5 x 3 = 15
13. Find a point on x axis which is equidistant from the points (7, -6) and (3,4)

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

15. Find the equation of a circle whose diameters are 2x-3y+12=0 and x+4y-5=0 and area is 154 square units.

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

17. Find the locus of a point which moves in such a way that the square of its distance from the point (3, -2) is numerically equal to its distance from the line 5x - 12y = 13

18. 4 x 5 = 20
19. Prove that the lines 4x+3y=10, 3x-4y=-5 and 5x+y=7 are concurrent.

20. Prove that the tangents to the circle x2+y2=169 at (5,12) and (12,-5) are perpendicular to each other.

21. An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How side is 2 m from the vertex of the parabola?

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