`A-=(-4,0),B-=(4,0)dotMa n dN` are the variable points of the y-axis such that `M` lies below `Na n dM N=4` . Lines `A Ma n dB N` intersect at `Pdot` The locus of `P` is a. `2x y-16-x^2=0` b. `2x y+16-x^2=0` c. `2x y+16+x^2=0` d. `2x y-16+x^2=0`

Let A (-4,0) ,B(4,0) Number of points c= (x,y) on circle x^2+y^2=16 such that area of triangle whose verties are A,B,C is positive integer 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 of fixed length 2 units moves so that its ends are on the positive x-axis and that part of the line x+y=0 which lies in the second quadrant. Then the locus of the midpoint of the line has equation. a. x^2+5y^2+4x y-1=0 b. x^2+5y^2+4x y+1=0 c. x^2+5y^2-4x y-1=0 d. 4x^2+5y^2+4x y+1=0

The equation of the line inclined at an angle of pi/4 to the x-axis ,such that the two circles x^2+y^2=4 and x^2+y^2 -10 x-14 y+65=0 intercept equal length on it, is (A) 2x-2y-3=0 (B) 2x-2y+3=0 (C) x-y+6=0 (D) x-y-6=0

Find the equation of straight line joining the points of intersection of the lines 3x+2y+1=0 and x+y=3 to the intersection of the lines y-x=1 and 2x+y+2=0

x+2y+4=0,3x=-4y-16

From the point A (0, 3) on the circle x^2+4x+(y-3)^2=0 a chord AB is drawn & extended to a M point such that AM=2AB. The equation of the locus of M is: (A) x^2 +8x+y^2 =0 (B) x^2+8x+(y-3)^2=0 (C) (x-3)^2+8x+y^2=0 (D) x^2+8x+8y^=0

The image of the pair of lines represented by a x^2+2h x y+b y^2=0 by the line mirror y=0 is a x^2-2h x y-b y^2=0 b x^2-2h x y+a y^2=0 b x^2+2h x y+a y^2=0 a x^2-2h x y+b y^2=0

Find the image of the circle x^2+y^2-2x+4y-4=0 in the line 2x-3y+5=0

A variable chord of the circle x^2+y^2=4 is drawn from the point P(3,5) meeting the circle at the point A and Bdot A point Q is taken on the chord such that 2P Q=P A+P B . The locus of Q is (a) x^2+y^2+3x+4y=0 (b) x^2+y^2=36 (c) x^2+y^2=16 (d) x^2+y^2-3x-5y=0