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

If the chord u=mx +1 of the circel x ^(2) +y^(2)=1 subtends an angle of 45^(@) at the major segment of the circle, then the value of m is-

The line y = mx + 1 is a tangent to the curve y^(2) = 4x if the value of m is

Find the length of normal chord which subtends an angle of 90^0 at the vertex of the parabola y^2=4xdot

chord AB of the circle x^2+y^2=100 passes through the point (7,1) and subtends are angle of 60^@ at the circumference of the circle. if m_1 and m_2 are slopes of two such chords then the value of m_1*m_2 is

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 (2pi)/3 at its centre is x^2 + y^2-kx + y +31/16=0 then k is

A(x_(1) y_(1)) and B(x_(2), y_(2)) are two given points on a circle. If the chord AB substends an angle theta at a point p on its circumferene, show that the equation of the circle is (x-x_(1)) (x-x_(2))+(y-y_(1))(y-y_(2))=+- cos theta [ (x-x_(1))(y-y_(2))-(x-x_(2))(y-y_(1))]

If the straight line y=mx lies outside of the circle x^(2)+ y^(2) - 20y + 90 =0 , then the value of m will satisfy

The length of the chord cut off by y=2x+1 from the circle x^2+y^2=2 is

If the straight line y = mx is outside the circle x^2+y^2-20y+90=0 , then

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