`y^2-4y-1=0`

A line of fixed length 2 units moves so that its ends are on the positive x-axis and that part of the line x+y=0 which lies in the second quadrant. Then the locus of the midpoint of the line has equation. (a) x^2+5y^2+4x y-1=0 (b) x^2+5y^2+4x y+1=0 (c) x^2+5y^2-4x y-1=0 (d) 4x^2+5y^2+4x y+1=0

A line of fixed length 2 units moves so that its ends are on the positive x-axis and that part of the line x+y=0 which lies in the second quadrant. Then the locus of the midpoint of the line has equation. a. x^2+5y^2+4x y-1=0 b. x^2+5y^2+4x y+1=0 c. x^2+5y^2-4x y-1=0 d. 4x^2+5y^2+4x y+1=0

Find the parametric representation of the following circle x^2 + y^2+2x-4y-1=0 .

If y=e^(ex) (ax+b) , show that y^2-4y_1+4y=0

Find the equation of the radical axis of the following circles. x^2+y^2-2x-4y-1=0 x^2+y^2-4x-6y+5=0

Find the equation of the radical axis of the following circles. x^2+y^2-2x-4y-1=0 x^2+y^2-4x-6y+5=0

If the equation 2x^(2)+kxy-3y^(2)-x-4y-1=0 represents a pair of lines then the value of ' 'k' can be:

At what points on the curve x^(2)+y^(2)-2x-4y+1=0, the tangents are parallel to the y-a is?

The circles x^(2)+y^(2)-2x-4y+1=0 and x^(2)+y^(2)+4y+4x-1 =0