Find the hyperbola whose asymptotes are 2x – y = 3 and 3x + y – 7 = 0 and which passes through the point (1, 1).
The equation of the hyperbola differs from the equation of the asymptotes by a constant.
The equation of the hyperbola with asymptotes 3x + y – 7 = 0
and 2x – y = 3 is
(3x + y – 7)(2x – y – 3) + k = 0
It passes through (1, 1) k = – 6
Hence the equation of the hyperbola is
(3x + y – 7)(2x – y – 3) = 6
Let two perpendicular chords of the ellipse each passing through exactly one of the foci meet at a point P. If from P two tangents are drawn to the hyperbola , then
If x = 9 is the chord of contact of the hyperbola x2 – y2 = 9, then the equation of the corresponding pair of triangle is.
Find the equations of tangents to the hyperbola x2 – 4y = 36 which are perpendicular to the line x – y + 4 = 0
Find the coordinates of foci, the eccentricity and latus rectum. Determine also the equation of its directrices for the hyperbola
4x2 – 9y2 =36.
Find the distance from A(4, 2) to the points in which the line 3x – 5y = 2 meets the hyperbola xy = 24. Are these points on the same side of A?
The asymptotes of the hyperbola makes an angle 600 with x-axis. Write down the equation of determiner conjugate to the diameter y = 2x.
Two straight lines pass through the fixed points and have gradients whose product is k > 0. Show that the locus of the points of intersection of the lines is a hyperbola.
Find the equation of the triangles drawn from the point (–2, –1) to the hyperbola 2x2 – 3y2 = 6.
Find the range of ‘a’ for which two perpendicular tangents can be drawn to the hyperbola from any point outside the hyperbola
The locus of a variable point whose distance from (–2, 0) is times its distance from the line , is