The image of line `2x+y=1` in line `x+y+2=0` is : (A) `x+2y-7=0` (B) `2x+y-7=0` (C) `x+2y+7=0` (D) `2x+y+7=0`

The equation of straight line belonging to both the families of lines (x-y+1)+lambda_1(2x-y-2)=0 and (5x+3y-2)+lambda_2(3x-y-4)=0 where lambda_1, lambda_2 are arbitrary numbers is (A) 5x -2y -7=0 (B) 2x+ 5y - 7= 0 (C) 5x + 2y -7 =0 (D) 2x- 5y- 7= 0

The image of plane 2x-y+z=2 in the plane mirror x+2y-z=3 is (a) x+7y-4x+5=0 (b) 3x+4y-5z+9=0 (c) 7x-y+2z-9=0 (d) None of these

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

Equation of line touching both parabolas y^(2)=4x and x^(2) = -32y is a) x+2y + 4 =0 b) 2x +y4 =0 c) x-2y-4 =0 d) x-2y+4 =0

The equation of the plane passing through the point (1,1,-1) and perpendicular to the planes x+2y+3z-7=0 and 2x-3y+4z=0 is (a) 17 x+2y-7z=26 (b) 17 x-2y+7z=26 (c) 17 x+2y-7z+26=0 (d) 17 x-2y+7z+26=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

The equation of the ellipse whose focus is (1, -1) , directrix is the line x-y-3=0 and eccentricity is 1/2 , is: (A) 7x^2 + 2xy + 7y^2 + 7 = 0 (B) 7x^2 + 2xy+7y^2 + 10x - 10y - 7 = 0 (C) 7x^2 + 2xy + 7y^2 - 10x + 10y + 7 = 0 (D) none of these

The locus of the mid-point of a chord of the circle x^2 + y^2 -2x - 2y - 23=0 , of length 8 units is : (A) x^2 + y^2 - x - y + 1 =0 (B) x^2 + y^2 - 2x - 2y - 7 = 0 (C) x^2 + y^2 - 2x - 2y + 1 = 0 (D) x^2 + y^2 + 2x + 2y + 5 = 0

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

The equation of the line passing through the center and bisecting the chord 7x+y-1=0 of the ellipse (x^2)/1+(y^2)/7=1 is (a) x=y (b) 2x=y (c) x=2y (d) x+y=0