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#### Two Dimensional Analytical Geometry Book Back Questions

11th Standard

Reg.No. :
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Maths

Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
1. The equation of the locus of the point whose distance from y-axis is half the distance from origin is

(a)

x2+3y2=0

(b)

x2-3y2=0

(c)

3x2+y2=0

(d)

3x2-y2=0

2. Which of the following point lie on the locus of 3x2+3y2-8x-12y+17 = 0

(a)

(0,0)

(b)

(-2,3)

(c)

(1,2)

(d)

(0,-1)

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 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

5. The equation of the line with slope 2 and the length of the perpendicular from the origin equal to $\sqrt5$ is

(a)

x+2y=$\sqrt5$

(b)

2x+y=$\sqrt5$

(c)

2x+y=5

(d)

x+2y-5=0

6. 3 x 2 = 6
7. Find the locus of P, if for all values of $\alpha$ the co-ordinates of a moving point P is  (9 cos,$\alpha$ 9 sin $\alpha$)

8. 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.

9. The length L (in cm) of a copper rod is a linear function of its Celsius temperature C. In an experiment if L = 124.942 when C = 20 and. L = 125.134 when C = 110, express L in terms of C.

10. 3 x 3 = 9
11. Find the equation of the straight line parallel to 5x - 4y + 3 = 0 and having x-intercept 3.

12. A straight rod of length 8 units slides with its ends A and B always on the x and y axes respectively. Find the locus of the mid point of the line segment AB.

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

14. 2 x 5 = 10
15. 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.

16. If the points P(6,2) and Q(-2,1) and R are the vertices of a Δ PQR and R is the point on the locus of y=x2-3x+4, then find the equation of the locus of centroid of Δ PQR