Find the locus of the foot of perpendicular from the centre upon any normal to the hyperbola .
Normal at is
and equation of perpendicular to (i) and passes through origin is
Elimination Ï• from (i) and (ii), we will get the equation of locus of Q, as from (ii),
To find the equation of the hyperbola from the definition that hyperbola is the locus of a point which moves such that the difference of its distances from two fixed points is constant with the fixed point as foci.
Find the equation of the hyperbola whose directrix is 2x + y = 1, focus (1, 2) and eccentricity .
Find the eccentricity of the hyperbola whose latus rectum is half of its transverse axis.
Find the equation of the hyperbola whose foci are (6, 4) and (–4, 4) and eccentricity is 2.
Obtain the equation of a hyperbola with coordinate axes as principal axes given that the distances of one of its vertices from the foci are 9 and 1 units.
The foci of a hyperbola coincide with the foci of the ellipse . Find the equation of the hyperbola if its eccentricity is 2.
For what value of λ does the line y = 2x + λ touches the hyperbola
Find the equation of the tangent to the hyperbola x2 – 4y2 = 36 which is perpendicular to the line x – y + 4 = 0.
Find the equation and the length of the common tangents to hyperbola
Find the locus of the mid-points of the chords of the hyperbola which subtend a right angle at the origin.