Advertisements
Advertisements
प्रश्न
Find the equation of tangent to the parabola y2 = 36x from the point (2, 9)
उत्तर
Given the equation of the parabola is y2 = 36x.
Comparing this equation with y2 = 4ax, we get
4a = 36
∴ a = 9
Equation of tangent to the parabola y2 = 4ax having slope m is y = `"mx" + "a"/"m"`
Since the tangent passes through the point (2, 9),
9 = `2"m" + 9/"m"`
∴ 9m = 2m2 + 9
∴ 2m2 – 9m + 9 = 0
∴ 2m2 – 6m – 3m + 9 = 0
∴ 2m(m – 3) – 3(m – 3) = 0
∴ (m – 3)(2m – 3) = 0
∴ m = 3 or m = `3/2`
These are the slopes of the required tangents.
By slope point form, y – y1 = m(x – x1), the equations of the tangents are
y – 9 = 3(x – 2) and y – 9 = `3/2("x" - 2)`
∴ y – 9 = 3x – 6 and 2y – 18 = 3x – 6
∴ 3x – y + 3 = 0 and 3x – 2y + 12 = 0
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:
3x2 = 8y
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)
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 coordinates of the point on the parabola. Also, find focal distance.
2y2 = 7x whose parameter is –2
Find length of latus rectum of the parabola y2 = 4ax passing through the point (2, –6)
If a parabolic reflector is 20 cm in diameter and 5 cm deep, find its focus.
Find the equation of common tangent to the parabola y2 = 4x and x2 = 32y
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 focus of the parabola is (0, –3) its directrix is y = 3 then its equation is
Select the correct option from the given alternatives:
The coordinates of a point on the parabola y2 = 8x whose focal distance is 4 are _______
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 _________
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:
Find the Cartesian coordinates of the point on the parabola y2 = 12x whose parameter is −3
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:
Show that the two tangents drawn to the parabola y2 = 24x from the point (−6, 9) are at the right angle
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:
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
`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
The area of the triangle formed by the lines joining vertex of the parabola x2 = 12y to the extremities of its latus rectum is ______.
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 line `y - sqrt(3)x + 3` = 0 cuts the parabola y2 = x + 2 at A and B, then PA. PB is equal to `("where coordinates of P are" (sqrt(3), 0))` ______.
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 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 ______.
If vertex of a parabola is (2, –1) and the equation of its directrix is 4x – 3y = 21, then the length of its latus rectum is ______.
Area of the equilateral triangle inscribed in the circle x2 + y2 – 7x + 9y + 5 = 0 is ______.
