Consider the two curves  then

a)  touch each other at only one point

b)  touch each other exactly at two points

c)  intersect(but not touch) at exactly two points

d)  neither intersect nor touch each other

Find the equation to the hyperbola referred to the axes as axes of coordinate whose conjugate axis is 5 and the distance between whose foci is 13.

a) 144x² – 25y² = 900

b) 25x² – 144y² = 900

c) 25x² + 144y² = 900

d) 144x² – 25y² = 900

Find the equation to the hyperbola referred to the axes as axes of coordinate whose conjugate axis is 7 and which passes through the point (3, −2)

a) 49x² – 36y² = 441

b) 36x² – 49y² = 441

c) 65x² – 36y² = 441

d) 36x² – 65y² = 441

Find the equation to the hyperbola referred to the axes as axes of coordinate the distance between whose foci is 16 and whose eccentricity is .

a) 2x² – y² = 32

b) x² – 2y² = 32

c) 4x² – y² = 32

d) x² – y² = 32

In the hyperbola 4x² – 9y² = 36, find the axes, the coordinate of foci, the eccentricity and the latus rectum.

a)

b)

c)

d)

Find the equation to the hyperbola of given transverse axis whose vertex bisects the distance 2d between the centre and the focus.

a) 3x² – y² = d²

b) x² – 3y² = d²

c) 3x² – y² = 3d²

d) x² – 3y² = 3d²

Find the equation to the hyperbola whose eccentricity is , whose focus is (a, 0) and whose directrix is 4x – 3y = a.

a) 7x² – 7y² + 24xy – 24ax – 6ay + 15a² = 0

b) 7x² – 7y² + 24xy – 24ax – 6ay − 5a² = 0

c) 7y² + 24xy – 24ax – 6ay − 15a² = 0

d) 7y² + 24xy – 24ax – 6ay + 15a² = 0

Find the points common to the hyperbola 25x² – 9y² = 225 and the straight line 25x + 12y – 45 = 0.

a)

b)

c)

d)

Find the equation of the tangent to the hyperbola 4x² – 9y² = 1 which is parallel to the line 4y = 5x + 7.

a)  

b)  

c)  

d)  

The straight lines  and  always intersect on a ..............

a) Circle

b) Parabola

c) Ellipse

d) Hyperbola

In the hyperbola 16x² – 9y² = 144, find the equation to the diameter which is conjugate to the diameter whose equation is x = 2y.

a) 32y + 9x = 0

b) 9y + 32x = 0

c) 9y = 32x

d) 32y = 9x

Find the equation to the chord of the hyperbola 25x² – 16y² = 400 which is bisected at the point (5, 3).

a) 125x + 48y = 481

b) 125x – 48y = 481

c) 48x – 125y = 481

d) 48x + 125y = 481

In a rectangular hyperbola, prove that  

Show that in a rectangular hyperbola the distance of a point from the centre varies inversely as the perpendicular from the centre upon the polar.

The locus of the poles with respect to the parabola y² = 4ax of tangent to the hyperbola x² – y² = a² is ..............

a) x² + y² = 4a²

b) 4x² + y² = 4a²

c) x² + 4y² = 4a²

d) x² – 4y² = 4a²

The locus of the pole with respect to the hyperbola  of any tangent to the circle whose diameter is the line joining the foci is .............

a)

b)

c)

d)

From points on the circle x² + y² = a² tangents are drawn to the hyperbola x² – y² = a², prove that the locus of the middle points of the chord of contact is the curve (x² − y²)² = a² (x² + y²).

Chords of a hyperbola are drawn, all passing through the point (h, k); prove that the locus of the middle point is a hyperbola whose center is the point , and which is similar to either the hyperbola or its conjugate.

Through the positive vertex of the hyperbola  a tangent is drawn. Where does it meet the conjugate hyperbola?

a)  

b)

c)

d)

If e and e’ be the eccentricities of a hyperbola and its conjugate, then .............

a)

b)

c)

d)

Tangents are drawn to a hyperbola from any point on one of the branches of the conjugate hyperbola; show that their chord of contact will touch the other branch of the conjugate hyperbola.

Find the equation to the hyperbola, whose asymptotes are the straight lines x + 2y + 3 = 0 and 3x + 4y + 5 = 0 and which passes through the point (1, −1). Write down also the equation of the conjugate hyperbola.

a) 8x² + 5xy + 3y² + 22x + 14y + 15 = 0 and 8x² + 5xy + 3y² + 22x + 14y + 23 = 0

b) 3x² + 10xy + 8y² + 14x + 22y + 15 = 0 and 3x² + 10xy + 8y² + 14x + 22y + 23 = 0

c) 3x² + 8xy + 5y² + 7x + 15y + 15 = 0 and 3x² + 8xy + 5y² + 7x + 15y + 23 = 0

d) 8x² + 8xy + 8y² + 14x + 15y + 15 = 0 and 8x² + 8xy + 8y² + 14x + 15y + 23 = 0

If the ordinate NP at a point P of an ellipse be produced to Q, so that NQ is equal to the sub tangent of P, then the locus of Q is a ............

a) Ellipse

b) Parabola

c) Hyperbola

d) Circle