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

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

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

Let AB be a chord of the circle x^2+y^2=r^2 subtending a right angle at the center. Then the locus of the centroid of the Delta PAB as P moves on the circle is (1) A parabola (2) A circle (3) An ellipse (4) A pair of straight lines

If the segment intercepted by the parabola y^2=4a x with the line l x+m y+n=0 subtends a right angle at the vertex, then

If the chord y=m x+1 of the circles x^2+y^2=1 subtends an angle of 45^0 at the major segment of the circle, then the value of m is

The tangent at a point P(acosvarphi,bsinvarphi) of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 meets its auxiliary circle at two points, the chord joining which subtends a right angle at the center. Find the eccentricity of the ellipse.