Hyperbola Questions

For the hyperbola 4x2 − 9y2 = 1 which of the following are true

If 2x - y + 1 = 0 is a tangent to the hyperbola x2a2-y216=1, then which of the following CANNOT be sides of a right angled triangle ?...

Let P(6, 3) be a point on the hyperbola . If the normal at the point P intersects the x-axis at (9, 0), then the eccentricity of the hyperbola is...

The equation = 1, |r|

Let P (a sec θ, b tan θ) and Q(a sec φ, b tanφ), where θ + φ = , be two point on the hyperbola = 1. If (h, k) is the point of the intersection of the notmals at P and Q, ...

If x = 9 is the chord of contact of the hyperbola x2 - y2 = 9, then the equation of the corresponding pair of tangents is

The equation of hyperbola with vertices (-6,0) and (6,0) and semi latus rectum , is given by -

The eccentricity of the hyperbola 4x2 - 9y2 - 8x = 32 is -

The locus of the point of intersection of the lines √3x - y - 4 √3k = 0 and √3kx + ky - 4 √3 = 0 for different values of k is -

The vertices of a hyperbola are at (0, 0) and (10, 0) and one of its foci is at (18, 0) The possible equation of the hyperbola is -

AB is a double ordinate of the hyperbola = 1 such that ᐃAOB (where ′O′ is the origin) is an equilateral triangle, then the eccentricity e of the hyperbola satisfies -...

The equations to the common tangents to the two hyperbolas = 1 and = 1 are -...

The ellipse 4x2 + 9y2 = 36 and the hyperbola 4x2 - y2 = 4 have the same foci and they intersect at right angles then the equation of the circle through the points of intersection of two conics is -...

The equation of the common tangent to the parabola y2 = 8x and the hyperbola 3x2 - y2 = 3 is -

Equation of the chord of the hyperbola 25x2 - 16y2 = 400 which is bisected at the point (6, 2) is -

The asymptotes of the hyperbola xy - 3x - 2y = 0 are -

If the normal to the rectangular hyperbola xy = c2 at the point ′t′ meets the curve again at ′t1′ then t3t1 has the value equal to -If the normal to the rectangular hyperbola x...

Area of triangle formed by tangent to the hyperbola xy = 16 at (16, 1) and co-ordinate axes equals -

Locus of the middle points of the parallel chords with gradient m of the rectangular hyperbola xy = c2 is

Variable circles are drawn touching two fixed circles externally, then locus of centre of variable circle is -