Vertex of the parabola y² + 2y + x = 0 lies in the quadrant

The equation of the parabola with focus (3, 0) and the directrix x + 3 = 0 is

the locus of all points which are equidistant from a point called focus and a aline called directrix is known as a parabola. as per this definition, we can solve the  given question.

Length of the shortest normal chord of the parabola y² = 4x is-

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 common tangents to the circle x² + y² = a²/2 and the parabola y² = 4ax intersect at the focus of the parabola-

If on a given base triangle b be described such that the sum of the tangents of the base angles is constant (k), then the locus of third vertex is -

Set of values of ‘h’ for which the number of distinct common normals of (x – 2)² = 4(y – 3) and x² + y² – 2x – hy – c = 0 (c > 0) is 3, is -

PA and PB are the tangents drawn to y² = 4x from point P. These tangents meet the y-axis at the points A₁ and B₁ respectively. If the area of triangle PA₁ B₁ is 2 sq. units, then locus of ‘p’ is -

If the chord of contact of tangents from a point P to the parabola y² = 4ax, touches the parabola x² = 4by, then the locus of P is a/an -

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 -

Circle drawn having it’s diameter equal to focal distance of any point lying on the parabola x² – 4x + 6y + 10 = 0, will touch a fixed line whose equation is -

AB is a double ordinate of the parabola y² = 4ax. Tangents drawn to parabola at A and B meets y-axis at A₁ and B₁ respectively. If the area of trapezium AA₁ B₁ B is equal to 12a², then angle subtended by A₁B₁ at the focus of the parabola is equal to -

The parabola y² = 4x and the circle (x – 6)² + y² = r² will have no common tangent, if ‘r’ is equal to -

The name of the conic represented by the equation x² + y² – 2xy + 20x + 10 = 0 is-

From an external point P tangents are drawn to the parabola y² = 4ax, then the equation to the locus of P when these tangents makes angles θ₁ and θ₂ with the axis, such that tan θ₁ + tan θ₂ with the axis, such that tan θ₁ + tan θ₂ is constant (= b), is -

A point P (t², 2t) lies on the parabola y² = 4x, where FP is produced to B where F is focus. If PB = ƒ(t) and point B always lies on the line y – x = 2, then ƒ(t) is equal to-