Prove that all the having sum of the intercepts on the axes equal to half of the product of the intercepts pass through a fixed point. Also, find that fixed point.

Prove that all the lines having the sum of the interceps on the axes equal to half of the product of the intercepts pass through the point. Find the fixed point.

Find the normal to the curve x=a(1+costheta),y=asinthetaa tthetadot Prove that it always passes through a fixed point and find that fixed point.

Find the equation of the lines passing through the point (1,1) with y-intercept (-4)

Tangents are drawn from the points on the line x-y-5=0 to x^2+4y^2=4 . Then all the chords of contact pass through a fixed point. Find the coordinates.

A variable plane moves in such a way that the sum of the reciprocals of its intercepts on the coordinate axes is a constant. Show that the plane passes through a fixed point.

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).

A quadrilateral is inscribed in a parabola y^2=4a x and three of its sides pass through fixed points on the axis. Show that the fourth side also passes through a fixed point on the axis of the parabola.

Tangents are drawn to x^(2)+y^(2)=1 from any arbitrary point P on the line 2x+y-4=0 .Prove that corresponding chords of contact pass through a fixed point and find that point.

Tangents are drawn from the points on the line x-y-5=0 to x^(2)+4y^(2)=4 . Prove that all the chords of contact pass through a fixed point