Let `O` be the origin. If `A(1,0)a n dB(0,1)a n dP(x , y)` are points such that `x y >0a n dx+y<1,` then (a)`P` lies either inside the triangle `O A B` or in the third quadrant. (b)`P` cannot lie inside the triangle `O A B` (c)`P` lies inside the triangle `O A B` (d)`P` lies in the first quadrant only

Consider the points A(0,1)a n dB(2,0),a n dP be a point on the line 4x+3y+9=0 . The coordinates of P such that |P A-P B| is maximum are (-(24)/5,(17)/5) (b) (-(84)/5,(13)/5) ((31)/7,(31)/7) (d) (0,0)

If P(x , y) is any point on the line joining the point A(a ,0)a n dB(0, b), then show that x/a+y/b=1.

If points (a ,0),\ (0, b)a n d\ (x , y) are collinear, using the concept of slope prove that x/a+y/b=1.

If A=[[0,1],[-1,0]], find x\ a n d \ y such that (x I+y A)^2=A

Let (x , y) be such that sin^(-1)(a x)+cos^(-1)(y)+cos^(-1)(b x y)=pi/2dot Match the statements in column I with statements in column II Ifa=1a n db=0,t h e n(x , y) , (p) lies on the circle x^2+y^2=1 Ifa=1a n db=1,t h e n(x , y) , (q) l i e son(x^2-1)(y^2-1)=0 Ifa=1a n db=2,t h e n(x , y) , (r) lies on y=x Ifa=2a n db=2,t h e n(x , y) , (s) lies on (4x^2-1)(y^2-1)=0

If O Aa n dO B are equal perpendicular chords of the circles x^2+y^2-2x+4y=0 , then the equations of O Aa n dO B are, where O is the origin. 3x+y=0 and 3x-y=0 3x+y=0 and 3y-x=0 x+3y=0 and y-3x=0 x+y=0 and x-y=0

Let vec a , vec b , vec c be the position vectors of three distinct points A, B, C. If there exist scalars x, y, z (not all zero) such that x vec a+y vec b+z vec c=0a n dx+y+z=0, then show that A ,Ba n dC lie on a line.

Let (x,y) be any point on the parabola y^2 = 4x . Let P be the point that divides the line segment from (0,0) and (x,y) n the ratio 1:3. Then the locus of P is :

Let (x,y) be any point on the parabola y^2 = 4x . Let P be the point that divides the line segment from (0,0) and (x,y) n the ratio 1:3. Then the locus of P is :

A line passing through the origin O(0,0) intersects two concentric circles of radii aa n db at Pa n d Q , If the lines parallel to the X-and Y-axes through Qa n dP , respectively, meet at point R , then find the locus of Rdot