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

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 circle x^2+y^2=1 is completely contained in the circle x^2+y^2+4x+3y+k=0 , then find the values of kdot

The set of values of m for which it is possible to draw the chord y=sqrt(m)x+1 to the curve x^2+2x y+(2+sin^2alpha)^y^2=1 , which subtends a right angle at the origin for some value of alpha , is [2,3] (b) [0,1] [1,3] (d) none of these

The equation of the locus of the mid-points of chords of the circle 4x^2 + 4y^2-12x + 4y +1= 0 that subtends an angle of at its centre is (2pi)/3 at its centre is x^2 + y^2-kx + y +31/16=0 then k is

A circle of radius 5 units has diameter along the angle bisector of the lines x+y=2 and x-y=2. If the chord of contact from the origin makes an angle of 45^0 with the positive direction of the x-axis, find the equation of the circle.

If the circle x^2+y^2-4x-8y-5=0 intersects the line 3x-4y=m at two distinct points, then find the values of mdot

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__________

Find the length of the chord x^2+y^2-4y=0 along the line x+y=1. Also find the angle that the chord subtends at the circumference of the larger segment.

Let alpha chord of a circle be that chord of the circle which subtends an angle alpha at the center. If the slope of a pi//3 chord of x^(2)+y^(2)=4 is 1, then its equation is