L= 9x+7y+4 = 0. The locus of the centroid 2) 9x+7y+22=0 the lin vear 2D & 3D GEOMETRY 1.Locus and C' is of triangle ABC is the line 1) 3x EXERCISE -I 1) 9x 7y 22 =0 4) 27x+2ly-78=0 3) 2x A straight rod of length 31 unit slides with its ends A,B alwalys on the x and y axes respectively. Then the locus of the centroid. A line drawn through a fixed point (h, k) cuts 3) 27x+2ly-77=0 1. the axes at P and Q. The rectangle OPRQ is completed then the locus of R is 9. 15. If (p vert h k 2) -+-31 x y 1) h k ther 2) x + y = 1 4) x+y = 21 4) x-y=h-k is 3) x+y=h+k If a point P moves such that its distance from the point A(1, 1) and the line x +y + 2 =0 are equal, then the locus of P is 1) x +y? = 31 3) x +y = 41 2. 1) %3D 2) a pair of straight lines 10. Observe the following statements 4) a parabola 2) Statement-I: If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is a straight line Statement-II: The locus of a point P which divides the line joining (1,0) and (2 cos0,2 sin) internally in the ratio 2:3 for all values of 6 is 3. 1) a straight line (10s 3) an ellipse 4 3. If the point 'P' is equidistant from the points. A (1, 3), B( 3, 5) and C(5, 1) then PA = 16. 1) 5 2) 5/5 3) 25 4) 5/10 4. The ends of a rod of length I move on the a circle: coordinate axes. The locus of the point on the rod which divides it in the ratio 1: 2 is Which of the following is true? M 3) Both I and II 1) Only I 2) Only II 1) 36x 9y = 4( 3) 9x +36y = 4 The ends of the hypotenuse of a right angled 11. The locus of a point whose perpendicular 2) 36x +9y = ( 4) 9x +36y = 1 %3D %3D 4) Neither I nor II %3D 17. triangle are (0, 6) and (6, 0). The locus of its 1 distance is always units from 3x+4y-5=0 is third vertex is 15 1) x +y +6x+6y=0 2) x + y +6x-6y=0 3) x +y -6x +6y=0 4) x +y 6x -6y=0 O(0, 0), A (6, 0), B(0, 4) are three points. If P is a point such that area of A POB is twice the area of APOA , then the locus of P is 1) 3(4x-3y-5)=l 2) 3(3x+4y-5)=l 3) 3(4x+3y-5)=l 4) 3(3x4y-5)=l %3D %3D 12. A(2,3), B(1,5), C(-1,2) are three points. If P is 6. 2) 3x-4y=0 4) x-9y=0 a point which moves such that PA2+ PB=2PC", then locus of P is in the form ax+by+c=0.Then ascending order of a,b,c is 1) a,b,c 1) 4x-6y=0 3) 9x16y=0 2) b,c,a The locus of the point 7. 13. If A(3,0) and B(-3,0) are two points and 3) c,b,a (Cot 0+Cos0, Cot0-Cos0) where 0