### Eamcet - Maths - Parabola Test

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L and L’are ends of the latus rectum of the parabola x2 = 6y. the equation of OL and OL’ where O is the origin is

The equation of the common tangent to x2+ y2 = 8 and y2 = 16x is

The straight line x + y = k touches the parabola y = x-x2, if  k =

If (9,12) is one end of a double oridinate of the parabola y2 = 16x, then its equation is

I : If the points (2,-1), (5,k) are conjugate with respect to the parabola x2 = 8y then k = 7 II: If the lines 2x + 3y + 12 = 0,x – y + k = 0 are conjugate with respect to the parabola y2 = 8x then k = -12

If P (at21,2at1)and Q (at22,2at2),are variable points on the curve y2 = 4ax and PQ subtends a right angle at the vertex , than t1t2 =

If the equation of the parabola whose axis is parallel to x – axis and passing through (2,-1) (6,1) (3, -2) is ay2 + bx + cy + d = 0 then the ascending order of a,b,c,d is

The locus of the midpoint of chords of the parabola y2 = 4ax parallel to the line y = mx + c is

The length of the latus rectum of the parabola 3x2 – 9x + 5y – 2 = 0 is

The pole of the line 2x + 3y – 4 = 0 with respect to the parabola y2 = 4x is

the equation of the parabola whose axis is parallel to y –axis and passing through  is (-3,1), (1,1) is

If the vertex of the parabola y = x2 – 8x + c lies on x – axis, then the value of c is

The equation to the pair of tangents drawn from (3,-2) to the parabola y2 = x  is

A box contains 10 mangoes out of which 4 are rotten. Two mangoes are taken out together. If one of them is found to be good, the probability that the other is also good is

Through the vertex O of the parabola y2 = 4ax a perpendicular is drawn to any tangent meeting it at P and the parabola at Q.Then OP.OQ =

If the distance of two points P and Q on the parabola y2 = 4ax are 4 and 9 respectively,then 9  respectively,then the distance of the point of intersection of the tangents at P and Q fro the focus is

The length of the latus rectum of the parabola 4y2 + 12x – 20y + 67 = 0 is

The line y = x√2 + λ is a normal to the parabola y2 = 4ax, then λ =

The locus  of the point of intersection of perpendicular tangents to the parabola y2=4ax is

if the focus is (1,-1) and the directrix is the line x + 2y – 9 = 0, the vertex of the parabola is at

The tangents to the parabola y2 = 4ax at p (t1) and Q (t2) intersect at R. the area of Δ PQR is

The focus of a parabola is (2,3) and the foot of the perpendicular from the focus to the directrix is (4,5). The equation to the parabola is

The line y = m(x + a)+a/m touch the parabola y2= 4a(x+ a) form

The locus of the point of intersection of two tangents to the parabola y2 = 4ax which make an angle 300 with one another is

The tangent to y2 = ax makes an angle 450 with x- axis. Then its point of contact is

The equation of the axis of the parabola (y + 3)2 = 4(x – 2) is

The locus of the poles of chords of the parabola y2 = 4ax, which subtend a right angle at the vertex is

A straight line which makes equal intercepts on positive  X and Y axes and which is at a distance 1 unit from the origin intersects the straight line  y =2x+3+√2 at (x0, y0). Then 2x0+y0=

the equation of the parabola whose vertex is at (0,0) and focus is the point of intersection of x+y  =2, 2x –y = 4 is

The equation of the axis of the parabola 3x2 – 9x + 5y -2 = 0 is

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