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 locus  of the  midpoint its of chords of the hyperbola x2/a2-y2/b2=1 which pass through the positive end of the transverse axis is

  

  

  

  

The length of the conjugate axis of the hyperbola 9x2-16y2-18x-64y+89=0 is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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 asymptotes of a hyperbola are parallel to 2x + 3y = O and 3x+2y=0.  Its centre is at (1,  2) and it  passes through the point (5, 3).  Its equation is

  

  

  

  

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

  

  

  

  

If m1, m2 are slopes of the tangents to the hyperbola x2/25-y2/16=1 which pass through the point (6, 2) then

  

  

  

  

The equations of the tangents to the hyperbola 9x2-16y2 =144 at the ends of latus recta are

  

  

  

  

The equation of the hyperbola whose centre is (1,2), one focus is (6,2) and transverse axis 6 is

  

  

  

  

If the asymptotes of the hyperbola 14x2+38xy+20y2+x-7y-91=0 are 7x+5y-3=0, ax+by+c=0 then the descending order of a, b, c is

  

  

  

  

If the axes are rotated through an angle of 450 in the anticlockwise direction then the equation of rectangular hyperbola x2-y2=a2 changes to

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The equation to hyperbola whose centre is (0,0) distance between the foci is 18 and between the directrices is 8 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 equation of the normal to the hyperbola x2-4y2= 5  at (3,-1) is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

Tangents are drawn  from  the Point (-2, -1) to the hyperbola 2x2-3y2=6. Their equations are

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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