The locus of a point P(α, β) moving under the condition that the line y = αx + β is a tangent to the hyperbola
If y = αx + β touches the hyperbola , then
which represents a hyperbola.
Find the equation of the hyperbola whose asymptotes are x + 2y + 3 = 0 and 3x + 4y + 5 = 0 and which passes through the point
(1,–1 ). Find also the equation of the conjugate of the conjugate hyperbola.
The vertices of the hyperbola
The centre of the hyperbola
The eccentricity of the hyperbola with latusrectum 12 and semi-conjugate axis , is
The equation of the hyperbola with vertices (3, 0) and (–3, 0) and semi-latusrectum 4, is given by
The equation of the tangent to the curve 4x2 – 9y2 = 1 which is parallel to 4y = 5x + 7, is
The equation of the tangent parallel to y = x drawn to is
If m is a variable, the locus of the point of intersection of the lines is a/an
If the chords of contact of tangents from two points (x1, y1) and (x2, y2) to the hyperbola are at right angles, then is equal to
The equation of the chord joining two points (x1, y1) and (x2, y2) on the rectangular hyperbola xy = c2 is