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)
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 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
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