#### Two Dimensional Analytical Geometry - Important Question Paper

11th Standard

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Maths

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

Part A

10 x 1 = 10
1. Straight line joining the points (2, 3) and (-1, 4) passes through the point $(\alpha,\beta)$ if

(a)

$\alpha+2=7$

(b)

$3\alpha+\beta=9$

(c)

$\alpha+3\beta=11$

(d)

$3\alpha+\beta=11$

2. The slope of the line which makes an angle 45 with the line 3x- y = -5 are

(a)

1,-1

(b)

$\frac{1}{2},-2$

(c)

$1,\frac{1}{2}$

(d)

$2,-\frac{1}{2}$

3. Equation of the straight line that forms an isosceles triangle with coordinate axes in the I-quadrant with perimeter 4 + 2$\sqrt{2}$ is

(a)

x+y+2=0

(b)

x+y-2=0

(c)

$x+y-\sqrt{2}=0$

(d)

$x+y+\sqrt{2}=0$

4. The coordinates of the four vertices of a quadrilateral are (-2,4), (-1,2), (1,2) and (2,4) taken in order. The equation of the line passing through the vertex (-1,2) and dividing the quadrilateral in the equal areas is

(a)

x+1=0

(b)

x+y=1

(c)

x+y+3=0

(d)

x-y+3=0

5. The intercepts of the perpendicular bisector of the line segment joining (1, 2) and (3,4) with coordinate axes are

(a)

5,-5

(b)

5,5

(c)

5,3

(d)

5,-4

6. The locus of a moving point P(a cos3θ, a sin3θ) is

(a)

${ x }^{ \frac { 2 }{ 3 } }+{ y }^{ \frac { 2 }{ 3 } }={ a }^{ \frac { 2 }{ 3 } }$

(b)

x2+y2=a2

(c)

x + y = a

(d)

${ x }^{ \frac { 3 }{ 2 } }+{ y }^{ \frac { 3 }{ 2 } }={ a }^{ \frac { 3 }{ 2 } }$

7. AB = 12 cm. AB slides with A on x-axis, B on y-axis respectively. Then the radius of the circle which is the locus of ΔAOB, where O is origin is:

(a)

36

(b)

4

(c)

16

(d)

9

8. The equating straight line with y-intercept -2 and inclination with x-axis is 135° is:

(a)

x+y-2=0

(b)

y-x+2=0

(c)

y+x+2=0

(d)

none

9. The length of the perpendicular from origin to line is $\sqrt{3}x-y+24=0$ is:

(a)

2$\sqrt{3}$

(b)

8

(c)

24

(d)

12

10. If(1, 3) (2,1) (9, 4) are collinear then a is:

(a)

$\frac{1}{2}$

(b)

2

(c)

0

(d)

-$\frac{1}{2}$

11. Part B

6 x 2 = 12
12. If θ is a parameter, find the equation of the locus of a moving point, whose coordinates are x=a cos3, y=a sin3 θ.

13. Find the value of k and b, if the points P(-3,1) and Q(2,b) lie on the locus of x2 - 5x + ky= 0.

14. Find the equation of the locus of a point such that the sum of the squares of the distance from the points (3,5), (1,-1) is equal to 20.

15. If O is origin and R is a variable point on y2 = 4x, then find the equation of the locus of the mid-point of the line segment OR.

16. The coordinates of a moving point P are $(\frac{a}{2}(cosec\theta+sin\theta),\frac{b}{2}(cosec\theta-sin\theta))$ , where θ is a variable parameter. Show that the equation of the locus P is b2x2-a2y2=a2b2

17. The sum of the squares of the distances of a moving point from two fixed points (a, 0) and (-0, 0) is equal to 2c2. Find the equation to its locus.

18. Part C

6 x 3 = 18
19. Find the equation of the lines passing through the point (1,1)
(i) with y-intercept (-4)
(ii) with slope 3
(iii) and (-2, 3)
(iv) and the perpendicular from the origin makes an angle 60° with x- axis.

20. If p (r, c) is mid - point of a line segment between the axes, then show that $\frac{x}{r}+\frac{y}{c}=2$

21. If P is length of perpendicular from origin to the line whose intercepts on the axes are a and b , then show that $\frac{1}{p^2}=\frac{1}{a^2}+\frac{1}{b^2}$

22. The normal boiling point of water is 100°C or 212°F· and the freezing point of water is 0 °C or 32°F.
(i) Find the linear relationship between C and F.
(ii) Find the value of C for 98.6°F and
(iii) Find the value of F for 38°C.

23. Find the equation of the straight lines passing through (8, 3) and having intercepts whose sum is 1.

24. Show that the points (1, 3), (2, 1) and $(\frac{1}{2},4)$ are collinear, by using
(i) concept of slope
(ii) a straight line
(iii) any other method.

25. Part D

2 x 5 = 10
26. Show that the lines are 3x + 2y + 9 = 0 and 12x + 8y - 15 = 0 are paralle llines.

27. If (-4, 7) is one vertex of a rhombus and if the equation of one diagonal is 5x - y + 7 = 0, then find the equation of another diagonal.