Eamcet - Maths - Parabola Test

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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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