Parabola Questions

Let C be a circle and L a line on the same plane such that C and L do not intersect. Let P be a moving point such that the circle drawn with centre at P to touch L also touches C. Then the locus of P ...

Through the vertex O of the parabola, y2 = 4ax two chords OP and OQ are drawn and the circles on OP and OQ as diameter intersect in R. If θ1, θ2 and f are the angles made with the axis by th...

If two tangents drawn from a point P to the parabola y2 = 4x are at right angles, then the locus of P is

The area of the region bounded by the parabola (y - 2)2 = x - 1, the tangent to the parabola at the point (2, 3) and the x-axis is

A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at

The equation of a tangent to the parabola y2 = 8x is y = x + 2. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is...

The locus of the vertices of the family of parabolas y = is

The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S1, S2, S3 are respectively the areas of these parts numbered from top to botto...

A point on the parabola y2 = 18x at which the ordinate increases at twice the rate of the abscissa is

If a ≠ 0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y2 = 4ax and x2 = 4ay , then

The normal at the point (bt12, 2bt1) on a parabola meets the parabola again in the point (bt22,2bt2), then

The equation of lactus rectum of a parabola is x + y = 8 and the equation of the tangent at the vertex is x + y = 12, then length of L.R. is :-

The co-ordinates of a point on the parabola y2 = 8x whose focal distance is 4 is

If two tangents drawn from a point P to the parabola y2 = 4x be such that the slope of one tangent is double of the other, then P lies on the curve. :-

The area bounded by the parabola x2 = 8y & the line x - 2y + 8 = 0 is -

The line 2(x - a) + cy = 0 cuts the parabola y2 = 8x at P(2t12, 4t1) and Q(2t22, 4t2). If a∈ [2,4] and c ∈ R then t1t2 belongs to -...

The equation of image of parabola x2 = 4y with respect to line mirror x - y + 2 = 0 is -

If the focus of the parabola (y - λ)2 = 4(x - λ) always lies between the lines 2x + y = 1 and 2x + y = 3 then the sum of all integral values of λ is -...

A parabola passes through (1, 2) and (3, 4). The tangents drawn at these points intersect at (-6, 8), then the slope of directrix of the parabola is

Let O be the vertex and Q be any point on the parabola, x2 = 8y. If the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is :-...