The condition that the chord `xcosalpha+ysinalpha-p=0` of `x^2+y^2-a^2=0` may subtend a right angle at the center of the circle is _

The locus of the point, the chord of contact of which wrt the circle x^(2)+y^(2)=a^(2) subtends a right angle at the centre of the circle is

If the chord xcosalpha+ysinalpha=p of the hyperbola (x^2)/(16)-(y^2)/(18)=1 subtends a right angle at the center, and the diameter of the circle, concentric with the hyperbola, to which the given chord is a tangent is d , then the value of d/4 is__________

A normal chord of the parabola y^2=4ax subtends a right angle at the vertex if its slope is

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

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 (c ,0)dot

Find the locus of the mid-point of the chords of the circle x^2 + y^2 + 2gx+2fy+c=0 which subtend an angle of 120^0 at the centre of the circle.

The chord of the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 , whose equation is x cos alpha +y sin alpha =p , subtends a right angle at its centre. Prove that it always touches a circle of radius (ab)/sqrt(a^(2)-b^(2))

If the chord of contact of the tangents drawn from the point (h , k) to the circle x^2+y^2=a^2 subtends a right angle at the center, then prove that h^2+k^2=2a^2dot

A variable chord of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(b > a), subtends a right angle at the center of the hyperbola if this chord touches. a fixed circle concentric with the hyperbola a fixed ellipse concentric with the hyperbola a fixed hyperbola concentric with the hyperbola a fixed parabola having vertex at (0, 0).

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