Prove that infinitely many points lie on the line whose equation is `y=2x.`

Examine whether the following points lie on the locus whose equation is x^2+y^2+6x-6y-47=0 (5,2)

Examine whether the following points lie on the locus whose equation is x^2+y^2+6x-6y-47=0 (2,3)

Examine whether the following points lie on the locus whose equation is x^2+y^2+6x-6y-47=0 (1,-4)

Show that the points whose coordinates are (1,4) , (3,-2) and (-3,16) are on the same straight line . Write down the equation of the straight line on which the points lie Verify that this line is perpendicular to the line whose equation is 2x-6y+13=0 .

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

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

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

Equation of the separate lines of the pair of lines, whose equation is x^(2)-x y-12 y^(2)=0 are given by

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