Eamcet - Maths - Hyperbola Test

Test Instructions :

1. The Test is 1hr duration.
2. The Test Paper consists of 30 questions. The maximum marks are 30.
3. All the questions are multiple choice question type with three options for each question.
4. Out of the three options given for each question, only one option is the correct answer.
5. Each question is allotted 1 mark for each correct response.
6. 0.25 will be deducted for incorrect response of each question.
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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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