### Eamcet - Maths - Hyperbola Test

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The length of the latus rectum of the hyperbola 9x2-16y2+72x-32y-16=0 is

The foot of the normal 3x+4y=7 to the hyperbola 4x2-3y2=1 is

The locus of  the point of intersection of two tangents of the hyperbola x2/a2+y2/b2=1 which  make an angle 300 with one another is

If the equation of the hyperbola whose focus is (2, 4), eccentricity is 5 and directrix is 4x-3y+1=0 is 15x2-24xy+8y2+ax+by+c=0 then the ascending order of a, b, c is

The centre of the hyperbola 9x2-16y2+72x-32y-16=0 is

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

A line through the origin meets the circle x2+y2=a2 at P and the hyperbola x2-y2=a2 at Q. The locus the point of  intersection of the tangent at P to the circle and with the tangent t Q to the hyperbola is

The equations of the tangents to the hyperbola 2x2-3y2=6 which are perpendicular to the line x-2y+5 =0 are

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

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

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

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

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

The curve represented by x=a(cosh θ+sinh θ), y=b(cosh θ-sinh θ) is

The equation of the director circle of x2/12-y2/8=1 is

The equations of the tangents to the hyperbola 3x2-4y2=12 which are parallel to the line 2x+y+7 =0 are

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

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

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

The equation of  the transverse and conjugate axes of a hyperbola are respectively. X+2y-3=0, 2x-y+4=0 and their respective lengths are  √2 and 2/√3. The equation of the hyperbola is

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

The equation to one asymptote of the hyperbola 14x2+38xy+20y2+x-7y-91=0 is 7x+5y-3=0, then the other asymptote is

The equation of the hyperbola whose eccentricity 2 and foci are the foci of the ellipse x2/25 +y2/9 =1 is

If the line 3x-y =k is a hyperbola 3x2-y2=3, then k=

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

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

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

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

The locus  of the  midpoint its of chords of x2/a2-y2/b2=1 which pass through the focus (ae, 0) is

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