A to Z Exams

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 normal at P cuts the axis of the parabola y2 = 4ax in G and S is the focus of the parabola.If Δ SPG is equilateral then each side is of length

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

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 =

The point on the parabola y2 = 36x whose oridinate is three times its abscissa is

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

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

The locus of the point of intersection of two tangents to the parabola y2 = 4ax which intercept a constant length d on the directrix is

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

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

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

The length of the chord intercepted bt the parabola y = x2 + 3x  on the line x + y = 5 is

AB is a chord of the parabola y2 = 4ax with vertex at A. BC is drawn perpendicular to AB meeting the axis at C.The projection of BC on the axis of the parabola is

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

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 a circle cuts the parabola y2 = 4ax in four points, then the algebraic sum of oridinates of the four points 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

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

The equation of the parabola  with latusrectum joining the points (6,7) and (6,-1) is

The sum of the slopes of the tangents to the parabola y2 = 8x drawn from the point (-2,3) is

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

The equation of the tangents drawn from (3,2)  to the parabola x2 = 4y are

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)  

The equation of the tangent to the parabola y2 = 8x and which is parallel to the line x – y + 3 = 0

If the points (2,4), (k,6) are conjugate with respect to the parabola y2 = 4x then k =

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

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

The point on the parabola y = x2 + 7x + 2 closest to the line y = 3x – 3 is