Parabola · Mathematics · WB JEE

The two parabolas x² = 4y and y² = 4x meet in two distinct points. One of these is the origin and the other is

The vertex of the parabola x² + 2y = 8x $$-$$ 7 is

If P(at², 2at) be one end of a focal chord of the parabola y² = 4ax, then the length of the chord is

The length of the common chord of the parabolas y² = x and x² = y is

The coordinates of the focus of the parabola described parametrically by x = 5t² + 2, y = 10t + 4 are

If t₁ and t₂ be the parameters of the end points of a focal chord for the parabola y² = 4ax, then which one is true?

The vertex of the parabola y² + 6x $$-$$ 2y + 13 = 0 is

The coordinates of a moving point P are (2t² + 4, 4t + 6). Then its locus will be a/an

The locus of the middle points of all chords of the parabola y² = 4ax passing through the vertex is

$$\triangle \mathrm{OAB}$$ is an equilateral triangle inscribed in the parabola $$\mathrm{y}^2=4 \mathrm{a} x, \mathrm{a}>0$$ with O as the vertex, then the length of the side of $$\triangle \mathrm{O A B}$$ is

Let A be the point (0, 4) in the xy-plane and let B be the point (2t, 0). Let L be the midpoint of AB and let the perpendicular bisector of AB meet the y-axis M. Let N be the midpoint of LM. Then locus of N is

Let O be the vertex, Q be any point on the parabola x$$^2$$ = 8y. If the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is :

From the focus of the parabola $${y^2} = 12x$$, a ray of light is directed in a direction making an angle $${\tan ^{ - 1}}{3 \over 4}$$ with x-axis. Then the equation of the line along which the reflected ray leaves the parabola is

The point of contact of the tangent to the parabola y² = 9x which passes through the point (4, 10) and makes an angle $$\theta$$ with the positive side of the axis of the parabola where tan$$\theta$$ > 2, is

A line passes through the point $$( - 1,1)$$ and makes an angle $${\sin ^{ - 1}}\left( {{3 \over 5}} \right)$$ in the positive direction of x-axis. If this line meets the curve $${x^2} = 4y - 9$$ at A and B, then |AB| is equal to

Let P be a point on (2, 0) and Q be a variable point on (y $$-$$ 6)² = 2(x $$-$$ 4). Then the locus of mid-point of PQ is

AB is a chord of a parabola y² = 4ax, (a > 0) with vertex A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the axis of the parabola is

From the point ($$-$$1, $$-$$6), two tangents are drawn to y² = 4x. Then the angle between the two tangents is

Let the tangent and normal at any point P(at², 2at), (a > 0), on the parabola y² = 4ax meet the axis of the parabola at T and G respectively. Then the radius of the circle through P, T and G is

If P₁P₂ and P₃P₄ are two focal chords of the parabola y² = 4ax then the chords P₁P₃ and P₂P₄ intersect on the

If the tangent to the parabola y = x(2 $$-$$ x) at the point (1, 1) intersects the parabola at P. Find the co-ordinate of P.

Prove that for all values of m, except zero the st. line $$y = mx + {a \over m}$$ touches the parabola y² = 4ax

Find the angle subtended by the double ordinate of length 2a of the parabola y² = ax at its vertex.