Advertisements
Advertisements
Question
Answer the following:
Find the equation of the tangent to the parabola y2 = 8x at t = 1 on it
Advertisements
Solution
Given equation of the parabola is y2 = 8x
Comparing this equation with y2 = 4ax, we get
4a = 8
∴ a = `8/4` = 2
t = 1
Equation of tangent with parameter t is
yt = x + at2
∴ The equation of tangent with t = 1 is
y(1) = x + 2(1)2
∴ y = x + 2
∴ x – y + 2 = 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:
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 (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
For the parabola y2 = 4x, find the coordinate of the point whose focal distance is 17
Find the equation of tangent to the parabola y2 = 12x from the point (2, 5)
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:
Equation of the parabola with vertex at the origin and directrix x + 8 = 0 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 _________
Select the correct option from the given alternatives:
If the parabola y2 = 4ax passes through (3, 2) then the length 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:
Find the co-ordinates of a point of the parabola y2 = 8x having focal distance 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:
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
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 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 ______.
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 ______.
The centre of the circle passing through the point (0, 1) and touching the parabola y = x2 at the point (2, 4) is ______.
Which of the following are not parametric coordinates of any point on the parabola y2 = 4ax?
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 ______.
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 ______.
