Advertisements
Advertisements
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:
3y2 = –16x
Advertisements
उत्तर
Given equation of the parabola is 3y2 = –16x.
∴ y2 = `-16/3"x"`
Comparing this equation with y2 = – 4ax, we get
4a = `16/3`
∴ a = `4/3`
Co-ordinates of focus are S(–a, 0), i.e., S`(-4/3, 0)`
Equation of the directrix is x – a = 0,
i.e., `"x" - 4/3` = 0 i.e., 3x – 4 = 0
Length of latus rectum = 4a = `4(4/3) = 16/3`
Co-ordinates of end points of latus rectum are (–a, 2a) and (–a, –2a), i.e., `(-4/3, 8/3)` and `(-4/3, -8/3)`.
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:
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 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 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 with vertex at the origin, axis along X-axis and passing through the point (2, 3)
Find coordinates of the point on the parabola. Also, find focal distance.
y2 = 12x whose parameter is `1/3`
Find coordinates of the point on the parabola. Also, find focal distance.
2y2 = 7x whose parameter is –2
Find the equation of tangent to the parabola y2 = 12x from the point (2, 5)
If the tangent drawn from the point (–6, 9) to the parabola y2 = kx are perpendicular to each other, find k
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 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:
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 `("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
`x^2/144 - y^2/25` = 1
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
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 ______.
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 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 ______.
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 ______.
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 ______.
A circle of radius 2 unit passes through the vertex and the focus of the parabola y2 = 2x and touches the parabola y = `(x - 1/4)^2 + α`, where α > 0. Then (4α – 8)2 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 ______.
Area of the equilateral triangle inscribed in the circle x2 + y2 – 7x + 9y + 5 = 0 is ______.
