The straight line `y+x=1` touches the parabola (A) `x^2 + 4y = 0` (D) `x^2-x+y=0`(C) `4x^2-3x+y=0` (D) `x^2-2x+2y=0`

Find k for which the line x+2y+k=0 touches the parabola y^(2)+4y+4x=0

Show that the line 3x-4y=1 touches the circle x^(2)+y^(2)-2x+4y+1=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

Find the equations of the straight lines passing through the point (-3, 2) and making an angle of 45^(@ with the straight line 3x-y+4=0 (A) x-2y+7=0,2x+y+4= (B) x+2y+7=0,2x-y+4=0(c) x-2y-7=0,2x+y+4=0 (D) x-2y-7=0,2x+y-4=0

A parabola touches the coordinate axes at (25/3, 0) and (0, 25/4) . Equation of directrix of parabola is : (A) x+2y=0 (B) 2x+y=0 (C) 3x+4y=0 (D) 4x+3y=0

Consider the parabola P touching x-axis at (1,0) and y-axis (0,2). Directrix of parabola P is : (A) x-2y=0 (B) x+2y=0 (C) 2x-y=0 (D) 2x+y=0

Consider the parabola P touching x-axis at (1,0) and y-axis (0,2). Directrix of parabola P is : (A) x-2y=0 (B) x+2y=0 (C) 2x-y=0 (D) 2x+y=0

Three sides of a triangle are represented by lines whose combined equation is (2x+y-4) (xy-4x-2y+8) = 0 , then the equation of its circumcircle will be : (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

Three sides of a triangle are represented by lines whose combined equation is (2x+y-4) (xy-4x-2y+8) = 0 , then the equation of its circumcircle will be : (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 equation of common tangent at the point of contact of two parabola y^(2)=x and 2y=2x^(2)-5x+1 is x+y+1=0 (B) x+2y+1=0( C) x-2y-1=0( D )-x+2y-1=0