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प्रश्न
Select the correct option from the given alternatives:
The endpoints of latus rectum of the parabola y2 = 24x are _______
पर्याय
(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:
5y2 = 24x
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:
y2 = –20x
Find the equation of the parabola with vertex at the origin, axis along Y-axis and passing through the point (–10, –5).
Find the equation of the parabola whose vertex is O(0, 0) and focus at (–7, 0).
Find the equation of the parabola with vertex at the origin, axis along X-axis and passing through the point (1, –6)
Find the equation of the parabola with vertex at the origin, axis along X-axis and passing through the point (2, 3)
For the parabola 3y2 = 16x, find the parameter of the point (3, – 4).
For the parabola 3y2 = 16x, find the parameter of the point (27, –12).
Find the focal distance of a point on the parabola y2 = 16x whose ordinate is 2 times the abscissa
Find coordinates of the point on the parabola. Also, find focal distance.
y2 = 12x whose parameter is `1/3`
Find length of latus rectum of the parabola y2 = 4ax passing through the point (2, –6)
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.
Find coordinate of focus, vertex and equation of directrix and the axis of the parabola y = x2 – 2x + 3
Two tangents to the parabola y2 = 8x meet the tangents at the vertex in the point P and Q. If PQ = 4, prove that the equation of the locus of the point of intersection of two tangent is y2 = 8(x + 2).
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:
If the focus of the parabola is (0, –3) its directrix is y = 3 then its equation is
Answer the following:
Find the Cartesian coordinates of the point on the parabola y2 = 12x whose parameter is −3
Answer the following:
Find the equation of the tangent to the parabola y2 = 9x at the point (4, −6) on it
Answer the following:
Show that the two tangents drawn to the parabola y2 = 24x from the point (−6, 9) are at the right angle
Answer the following:
Find the equation of the tangent to the parabola y2 = 8x which is parallel to the line 2x + 2y + 5 = 0. Find its point of contact
Answer the following:
A line touches the circle x2 + y2 = 2 and the parabola y2 = 8x. Show that its equation is y = ± (x + 2).
Answer the following:
The slopes of the tangents drawn from P to the parabola y2 = 4ax are m1 and m2, show that `("m"_1 /"m"_2)` = k, where k is a constant.
Answer the following:
The tangent at point P on the parabola y2 = 4ax meets the y-axis in Q. If S is the focus, show that SP subtends a right angle at Q
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
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
x2 − y2 = 16
The length of latus-rectum of the parabola x2 + 2y = 8x - 7 is ______.
The area of the triangle formed by the lines joining vertex of the parabola x2 = 12y to the extremities of its latus rectum is ______.
Let P: y2 = 4ax, a > 0 be a parabola with focus S. Let the tangents to the parabola P make an angle of `π/4` with the line y = 3x + 5 touch the parabola P at A and B. Then the value of a for which A, B and S are collinear is ______.
Let y = mx + c, m > 0 be the focal chord of y2 = –64x, which is tangent to (x + 10)2 + y2 = 4. Then, the value of `4sqrt(2)` (m + c) is equal to ______.
The centre of the circle passing through the point (0, 1) and touching the parabola y = x2 at the point (2, 4) is ______.
If the vertex = (2, 0) and the extremities of the latus rectum are (3, 2) and (3, –2) then the equation of the parabola 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 ______.
The cartesian co-ordinates of the point on the parabola y2 = –16x, whose parameter is `1/2`, are ______.
