Advertisements
Advertisements
Question
Find the equation of tangent to the parabola y2 = 36x from the point (2, 9)
Advertisements
Solution
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
RELATED QUESTIONS
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 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 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)
For the parabola 3y2 = 16x, find the parameter of the point (27, –12).
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.
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
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 _________
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:
Find the Cartesian coordinates of the point on the parabola y2 = 12x whose parameter is 2
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 equation of the tangent to the parabola y2 = 9x at the point (4, −6) on it
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
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 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 ______.
The equation to the line touching both the parabolas y2 = 4x and x2 = –32y 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 ______.
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 ______.
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 ______.
