Parabola - 2 - JEE MCQ

If normal at point P on parabola y² = 4ax, (a > 0) meet it again at Q is such a way that OQ is of minimum length where O is vertex of parabola, then ΔOPQ is

If the tangent at the point P(x₁, y₁) to the parabola y² = 4ax meets the parabola y² = 4a(x + b) at Q and R, then the mid-point of QR is -

Tangents are drawn from a point P to the parabola y² = 8x such that the slope of one tangent is twice the slope of other. The locus of P is 

An equilateral triangle is inscribed in the parabola y² = 4x one of whose vertex is at the vertex of the parabola, the length of each side of the triangle is -

The parametric equation of a parabola is x = 4t², y = 8t. The tangents at the points whose parameters are 1/2 and 1 meet on the line -

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 locus of the point of intersection of the tangents to the parabola x² – 4x – 8y + 28 = 0 which are at right angles is

Chord of contact of two perpendicular tangents of parabola 3y² = 8x always passes a fixed point which is :

If tangent drawn from point P(2, 1) to the parabola y2 – 2y + 4x + 2 = 0 meet at A & B then area of ΔPAB is ?

The line y = 2x + c is a tangent to the parabola y² = 16 x, if c equals

If P (at₁², 2at₁) and Q (at₂², 2at₂) are two variable points on the curve y² = 4ax and PQ subtends a right angle at the vertex, then t₁t₂ is equal to -

The equation of the tangent to the parabola y = (x – 3)² parallel to the chord joining the points (3, 0) and (4, 1) is-

A tangent to the parabola y² = 4ax encloses an area of 4a² with the coordinate axes, the equation of the tangent is

R is a point inside the parabola y² = 4x and it divide the line segment PQ internally in λ : 1. If P is (1, 3) and Q is (1, 1), then the range of λ is

The general equation of 2nd degree 9x² –24xy + 16y2 – 20x –15y – 60 = 0 represents

If the line ax +by + c = 0 is a tangent to the parabola y² – 4y – 8x + 32 = 0, then –

A parabolic mirror is kept along y² = 4x and two light rays parallel to its axis, are reflected along one straight line. If one of the incident light rays is at 3 units distance from the axis, then the distance of other incident ray from axis will be

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

The locus of the mid point of the line segment joining the focus to a moving point on the parabola y² = 4ax is another parabola with directrix

Normals are drawn from the point P on a parabola y² = 4x with slopes m₁. m₂ = α is a part of the parabola it self, then the value of α is

If the normal to the curve x = t – 1, y = 3t² – 6 at the point (1, 6) make intercepts a and b on x and y-axis respectively, then the value of a + 12b is

Let P(x₁, y₁) and Q(x₂, y₂) be points on the curve y = x² – 5x + 6 at which the tangents drawn intersect at the pont R(1, 1). Find area of triangle PQR.

The value of P such that the vertex of y = x² + 2px + 13 is 4 unit above the x axis is -