`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`

Find the coordinates of the point of intersection of the lines 2x-y+3=0\ a n d\ x+2y-4=0.

Find the locus of the centre of the circle touching the line x+2y=0a n d x=2y

Locus of a point that is equidistant from the lines x+y-2=0a n dx+y-1=0 is (a) x+y-5=0 (b) x+y-3=0 (c) 2x+2y-3=0 (d) 2x+2y-5=0

The straight lines joining any point P on the parabola y^2=4a x to the vertex and perpendicular from the focus to the tangent at P intersect at Rdot Then the equation of the locus of R is (a) x^2+2y^2-a x=0 (b) 2x^2+y^2-2a x=0 (c) 2x^2+2y^2-a y=0 (d) 2x^2+y^2-2a y=0

A line intersects x-axis at A(2, 0) and y-axis at B(0, 4) . A variable lines PQ which is perpendicular to AB intersects x-axis at P and y-axis at Q . AQ and BP intersect at R . Locus of R is : (A) x^2 + y^2 - 2x + 4y = 0 (B) x^2 + y^2 + 2x + 4y = 0 (C) x^2 + y^2 - 2x - 4y=0 (D) x^2 + y^2 + 2x - 4y = 0

The lines x+2y+3=0,x+2y-7=0,a n d2x-y-4=0 are the sides of a square. The equation of the remaining side of the square can be (a) 2x-y+6=0 (b) 2x-y+8=0 (c) 2x-y-10=0 (d) 2x-y-14=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:

Find the point of intersection of the following pairs of lines: 2x-y+3=0\ a n d\ x+y-5=0

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 :