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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If the tangents and normals at the extremities of a focal chord of a parabola intersect at (x1,y1) and (x2,y2) respectively, then

  

  

  

  

The angles between tangents to the parabola y2 = 4ax at the points where it intersects with the line x – y –a = 0 is

  

  

  

  

The locus of the midpoint of the chords of the parabola y2= 6x which touch the circle x2 + y2 + 4x – 12 = 0 is

  

  

  

  

The equation of the common tangent to y2= 8x and x2+y2 – 12x + 4 = 0

  

  

  

  

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

  

  

  

  

If P is a point on the parabola y2 = 4ax such that the subtangent and subnormal at P are equal, then the coridinate of P are

  

  

  

  

The length of the focal chord of the parbola y2 = 4ax which makes an angle θ with its axis is

  

  

  

  

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 to the parabola having focus (-1,-1) and directrix 2x -3y +6 = 0 is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The vertex of a parabola is the point (a,b) and latusrectum is of length 1. If the axis of the parabola is along the positive direction of y – axis, then its equation is

  

  

  

  

The angle subtended at the focus by the normal chord of a parabola y2= 4ax at a point whose ordinate equal to abscisa is

  

  

  

  

The coordinate of the point on the parabola y2 = 2x whose focal distance is 5/2 are

  

  

  

  

If the lines 2x + 3y + 12 = 0,x – y + 4k = 0 are conjugate with respect to the parabola y2 = 8x then k =

  

  

  

  

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

  

  

  

  

The sub-tangent, ordinate and sub-normal to the parabola y2 = 4ax at a point ( diffferent from the origin ) are in

  

  

  

  

The equation to the normal to the parabola y2 = 4x at (1,2) is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

I .thev locusv of the midpoints of chords of the parabola y2 = 4ax which substends a right angle at the vertex is y2 = 2a (x – 4a) II. the locus of midpoint of chords of the parabola y2 = 4ax which touch the circle X2 + y2 = a2 is (y2- 2ax)2 = a2 (y2 + 4a2)  

  

  

  

  

AB,AC are tangents to a parabola y2= 4ax. If l1,l2,l3 are the lengths of perpendiculars from A,B,C on any tangent to the parabola,then

  

  

  

  

Match the following Parabola Focus y2 –x – 2y + 2 = 0 (1,2) y2 – 8x – 4y – 4 = 0 (-2,5) x2 + 4x – 8y + 28 = 0 (1,-1) x2 – 2x – 8y – 23 = 0 (5/4,1)

  

  

  

  

the equation of the parabola whose vertex is (3,-2) axis is parelle to x- axis and latus rectum 4 is

  

  

  

  

The locus of the point  of intersection of tangents to the parabola y2 = 4(x + 1) and y2 = 8(x+2) which are perpendicular to each other is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If z2 = (x1/2 + y1/2)/(x1/3 + y1/3), then x(∂z/∂x) + y(∂z/∂y) 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

  

  

  

  

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