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प्रश्न
Select the correct option from the given alternatives:
The endpoints of latus rectum of the parabola y2 = 24x are _______
विकल्प
(6, ±12)
(12, ±6)
(6, ±6)
none of these
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उत्तर
The endpoints of latus rectum of the parabola y2 = 24x are (6, ±12)
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संबंधित प्रश्न
Find co-ordinate of focus, equation of directrix, length of latus rectum and the co-ordinate of end points of latus rectum of the parabola:
3x2 = 8y
Find co-ordinate of focus, equation of directrix, length of latus rectum and the co-ordinate of end points of latus rectum of the parabola:
x2 = –8y
Find co-ordinate of focus, equation of directrix, length of latus rectum and the co-ordinate of end points of latus rectum of the parabola:
3y2 = –16x
Find the equation of the parabola with vertex at the origin, axis along X-axis and passing through the point (1, –6)
For the parabola 3y2 = 16x, find the parameter of the point (27, –12).
Find coordinates of the point on the parabola. Also, find focal distance.
y2 = 12x whose parameter is `1/3`
Find the area of the triangle formed by the line joining the vertex of the parabola x2 = 12y to the end points of latus rectum.
If a parabolic reflector is 20 cm in diameter and 5 cm deep, find its focus.
Find the equation of tangent to the parabola y2 = 36x from the point (2, 9)
Find the equation of common tangent to the parabola y2 = 4x and x2 = 32y
A circle whose centre is (4, –1) passes through the focus of the parabola x2 + 16y = 0.
Show that the circle touches the directrix of the parabola.
Select the correct option from the given alternatives:
The length of latus rectum of the parabola x2 – 4x – 8y + 12 = 0 is _________
Select the correct option from the given alternatives:
If the parabola y2 = 4ax passes through (3, 2) then the length of its latus rectum is ________
Answer the following:
For the following parabola, find focus, equation of the directrix, length of the latus rectum, and ends of the latus rectum:
2y2 = 17x
Answer the following:
Find the Cartesian coordinates of the point on the parabola y2 = 12x whose parameter is 2
Answer the following:
Find the co-ordinates of a point of the parabola y2 = 8x having focal distance 10
Answer the following:
Find the equations of the tangents to the parabola y2 = 9x through the point (4, 10).
Answer the following:
The slopes of the tangents drawn from P to the parabola y2 = 4ax are m1 and m2, show that m1 − m2 = k, where k is a constant.
Answer the following:
Find the
(i) lengths of the principal axes
(ii) co-ordinates of the foci
(iii) equations of directrices
(iv) length of the latus rectum
(v) Distance between foci
(vi) distance between directrices of the curve
16x2 + 25y2 = 400
The length of latus-rectum of the parabola x2 + 2y = 8x - 7 is ______.
The locus of the mid-point of the line segment joining the focus of the parabola y2 = 4ax to a moving point of the parabola, is another parabola whose directrix is ______.
If the three normals drawn to the parabola, y2 = 2x pass through the point (a, 0)a ≠ 0, then' a' must be greater than ______.
Let the tangent to the parabola S: y2 = 2x at the point P(2, 2) meet the x-axis at Q and normal at it meet the parabola S at the point R. Then, the area (in sq.units) of the triangle PQR is equal to ______.
If the normal at the point (1, 2) on the parabola y2 = 4x meets the parabola again at the point (t2, 2t), then t is equal to ______.
Which of the following are not parametric coordinates of any point on the parabola y2 = 4ax?
The equation to the line touching both the parabolas y2 = 4x and x2 = –32y is ______.
Through the vertex O of parabola y2 = 4x, chords OP and OQ are drawn at right angles to one another, where P and Q are points on the parabola. If the locus of middle point of PQ is y2 = 2(x – l), then value of l is ______.
The equation of the line touching both the parabolas y2 = x and x2 = y is ______.
Let a variable point A be lying on the directrix of parabola y2 = 4ax (a > 0). Tangents AB and AC are drawn to the curve where B and C are points of contact of tangents. The locus of centroid of ΔABC is a conic whose length of latus rectum is λ, then `λ/"a"` is equal to ______.
Two parabolas with a common vertex and with axes along x-axis and y-axis, respectively, intersect each other in the first quadrant. if the length of the latus rectum of each parabola is 3, then the equation of the common tangent to the two parabolas is ______.
The cartesian co-ordinates of the point on the parabola y2 = –16x, whose parameter is `1/2`, are ______.
