Eamcet - Maths - Parabola 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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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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