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A point P moves such that the difference between its distance from the origin and from the axis of x is always a constant c. The locus of P is a

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Important Questions on Conic Sections

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Mathematics>Coordinate Geometry>Conic Sections>Parabola
The equation of the latus rectum of a parabola is x+y=8 and the equation of the tangent at the vertex is x+y=12. Then, the length of the latus rectum is
EASY
Mathematics>Coordinate Geometry>Conic Sections>Parabola
The vertex of the parabola y=(x-2)(x-8)+7 is
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Mathematics>Coordinate Geometry>Conic Sections>Parabola
The directrix of the parabola 2y2+25x=0 is _________
HARD
Mathematics>Coordinate Geometry>Conic Sections>Parabola
The equation of the lines joining the vertex of the parabola y2=6x to the point on it which have abscissa 24 are
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Mathematics>Coordinate Geometry>Conic Sections>Parabola
The centres of those circles which touch the circle, x2+y2-8x-8y-4=0, externally and also touch the x - axis, lie on
HARD
Mathematics>Coordinate Geometry>Conic Sections>Parabola
Equation of the directrix of the parabola whose focus is (0,0) and the tangent at the vertex is x-y+1=0 is
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Mathematics>Coordinate Geometry>Conic Sections>Parabola
The equation y2+3=22x+y represents a parabola with the vertex at
EASY
Mathematics>Coordinate Geometry>Conic Sections>Parabola
A parabola y2=32x is drawn. From its focus, a line of slope 1 is drawn. The equation of the line is
MEDIUM
Mathematics>Coordinate Geometry>Conic Sections>Parabola
If one end of a focal chord of the parabola, y2=16x is at 1,4, then the length of this focal chord is
MEDIUM
Mathematics>Coordinate Geometry>Conic Sections>Parabola
The equation of the directrix of the parabola x2-4x-3y+10=0 is
EASY
Mathematics>Coordinate Geometry>Conic Sections>Parabola
The length of the Latus rectum of the parabola x=ay2+by+c is
HARD
Mathematics>Coordinate Geometry>Conic Sections>Parabola
Suppose the parabola (y-k)2=4(x-h), with vertex A, passes through O=(0, 0) and L=(0, 2). Let D be an end point of the latus rectum. Let the y-axis intersect the axis of the parabola at P. Then ∠PDA is equal to
EASY
Mathematics>Coordinate Geometry>Conic Sections>Parabola
Let a parabola P be such that its vertex and focus lie on the positive x-axis at a distance 2 and 4 units from the origin, respectively. If tangents are drawn from O(0,0) to the parabola P which meet P at S and R, then the area (in sq. units) of ΔSOR is equal to :
EASY
Mathematics>Coordinate Geometry>Conic Sections>Parabola
The two ends of a latus rectum of a parabola are (5,8) and (-7,8) . Then its focus is
HARD
Mathematics>Coordinate Geometry>Conic Sections>Parabola
An equilateral triangle is inscribed in the parabola y2=4ax, where one vertex of the triangle is at the vertex of the parabola. The length of the side of the triangle is
MEDIUM
Mathematics>Coordinate Geometry>Conic Sections>Parabola
In which of these cases, the parabola generated by the given pair of directrix and focus will be a degenerate case?
HARD
Mathematics>Coordinate Geometry>Conic Sections>Parabola
What will be the area of the triangle formed by the lines joining the vertex of the parabola y2=28x to the ends of its latus rectum?
EASY
Mathematics>Coordinate Geometry>Conic Sections>Parabola
The vertex of the parabola y=x2-2x+4 is shifted p units to the right and then q units up. If the resulting point is (4,5), then the values of p and q respectively are
HARD
Mathematics>Coordinate Geometry>Conic Sections>Parabola
A chord is drawn through the focus of the parabola y⁡ 2 = 6 x⁡  such that its distance from the vertex of this parabola is 5 2 , then its slope can be 
HARD
Mathematics>Coordinate Geometry>Conic Sections>Parabola
If PQ be a double ordinate of the parabola, y2=-4x, where P lies in the second quadrant. If R divides PQ in the ratio 2:1, then the locus of R is: