In how many points the line `y+14=0` cuts the curve whose equation is `-x(x^2+x+1)=0?`

In how many points the line y + 14 = 0 cuts the curve whose equation is x(x^(2) + x + 1) + y = 0 ?

If the straight line x+y=k cut the curve whose equation is x^(2)+y^(2)-4x-4y+3=0 at two points.Then the sum of the possible values of k such that the lines joining the origin to the points of intersection subtends a right angle at the origin is: 0,0

If the straight line x+y=k cut the curve whose equation is x^(2)+y^(2)-4x-4y+3=0 at two points.Then the sum of the possible values of k such that the lines joining the origin to the points of intersection subtends a right angle at the origin is:

If the straight line x+y=k cut the curve whose equation is x^(2)+y^(2)-4x-4y+3=0 at two points.Then the sum of the possible values of k such that the lines joining the origin to the points of intersection subtends a right angle at the origin is:

If the straight line x+y=k cut the curve whose equation is x^(2)+y^(2)-4x-4y+3=0 at two points.Then the sum of the possible values of k such that the lines joining the origin to the points of intersection subtends a right angle at the origin is:

The slope of the tangent to the curve y=x^(2) -x at the point where the line y = 2 cuts the curve in the first quadrant, is

Equation of the tangent to the curve y=2x^(2)+5x , at the point where the line y=3 cuts the curve in the first quadrant , is

The triangle formed by the lines whose combined equation is (y^(2)-4xy-x^(2))(x+y-1)=0 is

Find whether the line 2x+y=3 cuts the curve 4x^(2)+y^(2)=5. Obtain the equations of the normals at the points of intersection.

Prove that (-1,4) is the orthocentre of the triangle formed by the lines whose equations are : x-y+1=0 , x-2y+4=0 and 9x-3y+1=0