### Eamcet - Maths - Hyperbola

The locus of poles of the lines with respect to the hyperbola  x2/a2-y2/b2=1 which touch the ellipse x2/α2+y2/β2=1is

A.  α2 x2/a4+ β2 y2/b4=1

B.  α2 x2/a4-β2 y2/b4=1

C.  α2 x2/a4+ α2 y2/b4=1

D.  α2 x2/a2+ β2 y2/b2=1

The equation of the auxiliary circle of x2/16-y2/25=1 is

A.  x2+y2=16

B.  x2+y2=9

C.  x2+y2=5

D.  x2+y2=15

If a hyperbola has one focus at the origin and its eccentricity is 2. One of the directries is x+y+1=0. Then the centre of the hyperbola is

A.  (-1, -1)

B.  (1, -1)

C.  (-2, -1)

D.  (2, 2)

The radius  of  the  auxiliary circle  of  the  hyperbola  x2/12-y2/9=1 is

A.  3

B.  4

C.  5

D.  1

If a hyperbola has one focus at the origin and its eccentricity is √2. One of the directries is x+y+1=0. Then the equations to its asymptotes are

A.  x-1=0, y-1=0

B.  x+1=0, y+1=0

C.  x+3=0, y+3=0

D.  x+2=0, y+2=0

Radius of the director circle of the hyperbola (x2/81) - (y2/36) = 1 is

A.  2√5

B.  √5

C.  3√5

D.  √5/2

The equation of the hyperbola with its axes as coordinate axes, whose transverse axis 8 and eccentricity 3/2 is

A.  x2/9-y2/4=1

B.  x2/16-y2/20=1

C.  x2/25-y2/11=1

D.  x2/16-y2/9=1

The conic represented by 2x2-12xy+23y2-4x-28y-48=0 is

A.  parabola

B.  Ellipse

C.  hyperbola

D.  none

A plane π makes intercepts 3 and 4 respectively on z-axis.If π is parallel to y-axis,then its equation is

A.  3x+4z =12

B.  3z+4x =12

C.  3y+4z =12

D.  3z+4y =12

If the latus rectum of a hyperbola x2/16-y2/p=1 is 41/2. If eccentricity e=

A.  4/5

B.  5/4

C.  3/4

D.  4/3

The length of the transverse axis of the hyperbola 4x2-9y2+8x+40=0 is

A.  4

B.  6

C.  2√3

D.  4√2

The locus of the point of intersection of tangents to the  hyperbola  x2-y2=a2 which includes an angle of 450 is

A.  (x2+y2)2=4a2 (x2+y2+a2)

B.  (x2+y2)2=4a2 (x2-y2+a2)

C.  (x2+y2)2=4a2 (y2-x2+a2)

D.  (x2+y2)2=4a2 (x2+y2-a2)

The conic represented by x2-4x+3y-1=0 is

A.  parabola

B.  Ellipse

C.  hyperbola

D.  none

The locus of poles of tangents to the hyperbola x2-y2=a2 w. r. t the parabola y2=4ax is

A.  x2+4y2=4a2

B.  x2-4y2=4a2

C.  4x2+y2=4a2

D.  4x2-y2=4a2

A normal to the hyperbola x2/a2-y2/b2=1 cuts the axes at K and L. The perpendiculars at K and L axes meet in P. The locus of P is

A.  a2x2+b2y2=(a2+b2)2

B.  a2x2-b2y2=(a2+b2)2

C.  a2x2+b2y2=(a2-b2)2

D.  a2x2-b2y2=(a2-b2)2

The equation of the asymptotes of the hyperbola 4x2-9y2=36 are

A.  2x±3y=0

B.  2x±5y=0

C.  2x±6y=0

D.  2x±8y=0

The sum and product of the slops of the tangents to the hyperbola 2x2-3y2=6 drawn from the point (-1,1) are

A.  1,-3

B.  1,-3/2

C.  2, -3/2

D.  3,-2/2

The length of latus rectum of parabola y2+8x-2y+17 = 0 is:

A.  2

B.  4

C.  8

D.  16

If 2x-ky+3=0, 3x-y+1=0 are conjugate lines with respect to 5x2-6y2=15 then k =

A.  2

B.  3

C.  4

D.  6

The equations of the tangents to the hyperbola 4x2-5y2 =20 which make an angle 900 with the transverse axis are

A.  y=√5x±√21

B.  y=√5x ±√11

C.  y=√7x ±√21

D.  y=√3x±√11

For a binominal variate X, if n = 4 and P(X = 4) = 6 P(X = 2), then the value of p is:

A.  3/7

B.  4/7

C.  6/7

D.  5/7

Tangents to x2/a2+y2/b2=1 make an angles θ1, θ2 with traverse axis. The equation of the locus of their intersection when cot (θ1+θ2)=k is

A.  k(x2-a2)=2xy

B.  k(y2+b2)=2xy

C.  k(x2+a2)=2xy

D.  k(y2-b2)=2xy

The polar of (-2, 3) w. r. t the hyperbola 4x2-3y2=12 is

A.  8x+3y-4=0

B.  8x+9y+12=0

C.  9x+8y-6=0

D.  8x+9y+7=0

PN is the ordinate of any point P on the hyperbola x2/a2 – y2/b2 =1. If Q divides AP in the ratio a2:b2 then NQ is

A.  perpendicular to A’P

B.  parallel to A’P

C.  perpendicular to OP

D.  none

The foci of the hyperbola 2x2-y2-4x+4y-10=0 are

A.  (±√13, 0)

B.  (1±2√3, 2)

C.  (2±3√3, 3)

D.  (3±3√3, 2)

If the normal at ‘θ’ on the hyperbola x2/a2-y2/b2=1 meets the tansverse axis at G, the AG, AG’=

A.  a2(e4 sec2 θ-1)

B.  a2(e4 sec2 θ+1)

C.  b2(e4 sec2 θ-1)

D.  none

The equations to the common tangents to the two hyperbolas x2/a2-y2/b2=1 and y2/a2-x2/b2=1Are

A.  y= ±x±√b2-a2

B.  y= ±x±√a2-b2

C.  y= ±x±(a2-b2)

D.  y= ±x±√a2+b2

The condition that the line x cos α + y sin α =p to be a tangent to the hyperbola x2/a2 -y2/b2 =1 is

A.  a2 cos2 α+ b2 sin2 α =p2

B.  a2 cos2 α- b2 sin2 α =p2

C.  a2 sin2 α+ b2 cos2 α =p2

D.  a2 sin2 α+ b2 cos2 α =p2

The equation of conjugate axis of the  hyperbola 5x2-4y2-30x-8y-30=0  is

A.  x=0

B.  x-3=0

C.  x-2=0

D.  x+3=0

The equation to the pair of asymptotes of the hyperbola 2x2-y2=1 is

A.  2x2+y2=0

B.  2x2-y2=0

C.  x2+2y2=0

D.  x2-2y2=0