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.

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

Find the locus of the midpoint of the chords of the circle x^2+y^2=a^2 which subtend a right angle at the point (0,0)dot

If two normals to a parabola y^2 = 4ax intersect at right angles then the chord joining their feet pass through a fixed point whose co-ordinates are:

A variable circle which always touches the line x+y-2=0 at (1, 1) cuts the circle x^2+y^2+4x+5y-6=0 . Prove that all the common chords of intersection pass through a fixed point. Find that points.

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.

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

Coordinates of points on curve 5x^(2) - 6xy +5y^(2) - 4 = 0 which are nearest to origin are

The tangent to the curve y=xe^(x^2) passing through the point (1,e) also passes through the point

Find the locus of the middle points of the chords of the parabola y^2=4a x which subtend a right angle at the vertex of the parabola.

Find the point on the curve 3x^2-4y^2=72 which is nearest to the line 3x+2y+1=0.