Advertisements
Advertisements
प्रश्न
Answer the following:
Find the Cartesian coordinates of the point on the parabola y2 = 12x whose parameter is −3
Advertisements
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:
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 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)
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.
Find the equation of tangent to the parabola y2 = 36x from the point (2, 9)
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 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 endpoints of latus rectum of the parabola y2 = 24x are _______
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 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:
Find the equation of the tangent to the parabola y2 = 8x at t = 1 on it
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
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 ______.
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 ______.
The equation to the line touching both the parabolas y2 = 4x and x2 = –32y 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 ______.
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 ______.
The equation of the line touching both the parabolas y2 = x and x2 = y is ______.
Area of the equilateral triangle inscribed in the circle x2 + y2 – 7x + 9y + 5 = 0 is ______.
