### Eamcet - Maths - Hyperbola Test

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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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