Advertisements
Advertisements
प्रश्न
Answer the following:
Find the Cartesian coordinates of the point on the parabola y2 = 12x whose parameter is −3
उत्तर
The equation of the parabola is y2 = 12x.
Comparing with y2 = 4ax, we get,
4a = 12
∴ a = 3
The point with parameter t is
P(t) ≡ (at2, 2at)
P(– 3) = (3 × 9, 2 × 3 × (– 3))
= (27, –18)
APPEARS IN
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:
y2 = –20x
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 the equation of the parabola with vertex at the origin, axis along X-axis and passing through the point (3, 4)
Find the equation of the parabola whose vertex is O(0, 0) and focus at (–7, 0).
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 coordinates of the point on the parabola. Also, find focal distance.
y2 = 12x whose parameter is `1/3`
For the parabola y2 = 4x, find the coordinate of the point whose focal distance is 17
If a parabolic reflector is 20 cm in diameter and 5 cm deep, find its focus.
Find coordinate of focus, vertex and equation of directrix and the axis of the parabola y = x2 – 2x + 3
Find the equation of tangent to the parabola y2 = 12x from the point (2, 5)
Find the equation of common tangent to the parabola y2 = 4x and x2 = 32y
Find the equation of the locus of a point, the tangents from which to the parabola y2 = 18x are such that some of their slopes is –3
Select the correct option from the given alternatives:
The line y = mx + 1 is a tangent to the parabola y2 = 4x, if m is _______
Select the correct option from the given alternatives:
The area of the triangle formed by the line joining the vertex of the parabola x2 = 12y to the endpoints of its latus rectum is _________
Select the correct option from the given alternatives:
The equation of the parabola having (2, 4) and (2, –4) as endpoints 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:
For the following parabola, find focus, equation of the directrix, length of the latus rectum, and ends of the latus rectum:
5x2 = 24y
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 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
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 equation of the directrix of the parabola 3x2 = 16y is ________.
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 ______.
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 ______.
If a line along a chord of the circle 4x2 + 4y2 + 120x + 675 = 0, passes through the point (–30, 0) and is tangent to the parabola y2 = 30x, then the length of this chord is ______.
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?
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 ______.
The equation of the parabola whose vertex and focus are on the positive side of the x-axis at distances a and b respectively from the origin is ______.
The equation of the line touching both the parabolas y2 = x and x2 = y is ______.
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 ______.
