The equation of the chord of the circle `x^2+y^2-3x-4y-4=0` , which passes through the origin such that the origin divides it in the ratio 4:1, is

Find the equation of the normal to the curve x^(2) = 4y which passes through the point (1, 2).

Find the equation of chord of the circle x^(2)+y^(2)-2x-4y-4=0 passing through the point (2,3) which has shortest length.

Solve (x^(2)-y) dx+(y^(2)-x)dy=0 , if it passes through origin :

Equation of the smaller circle that touches the circle x^2+y^2=1 and passes through the point (4,3) is

Find the equation of tangent to the hyperbola y=(x+9)/(x+5) which passes through (0, 0) origin

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

All chords.of the curve x^2+y^2-10x-4y+4=0 which make a right angle at (8,-2) pass through

The locus of centre of a circle which passes through the origin and cuts off a length of 4 units on the line x =3 is

Show that all chords of the curve 3x^2-y^2-2x+4y=0, which subtend a right angle at the origin, pass through a fixed point. Find the coordinates of the point.

The common chord of the circle x^2+y^2+6x+8y-7=0 and a circle passing through the origin and touching the line y=x always passes through the point. (-1/2,1/2) (b) (1, 1) (1/2,1/2) (d) none of these