English
Tamil Nadu Board of Secondary EducationHSC Science Class 12

Find the equation of the parabola in the cases given below: Passes through (2, – 3) and symmetric about y-axis - Mathematics

Advertisements
Advertisements

Question

Find the equation of the parabola in the cases given below:

Passes through (2, – 3) and symmetric about y-axis

Sum
Advertisements

Solution


x2 = 4ay

It passes through (2, – 3)

⇒ 22 = 4a(– 3)

4 = – 12a

⇒ a = `- 1/3`

⇒ 4a = `- 4/3`

∴ Equation of parabola is x2 = `- 4/3`y

3x2= – 4y

shaalaa.com
Conics
  Is there an error in this question or solution?
Chapter 5: Two Dimensional Analytical Geometry-II - Exercise 5.2 [Page 196]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 12 TN Board
Chapter 5 Two Dimensional Analytical Geometry-II
Exercise 5.2 | Q 1. (ii) | Page 196

RELATED QUESTIONS

Find the vertex, focus, axis, directrix, and the length of the latus rectum of the parabola y2 – 8y – 8x + 24 = 0.


Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola

x2 = 8y


The focus of the parabola x2 = 16y is:


Find the equation of the parabola in the cases given below:

Focus (4, 0) and directrix x = – 4


Find the equation of the parabola in the cases given below:

End points of latus rectum (4, – 8) and (4, 8)


Find the equation of the ellipse in the cases given below:

Length of latus rectum 4, distance between foci `4sqrt(2)`, centre (0, 0) and major axis as y-axis


Find the equation of the hyperbola in the cases given below:

Foci (± 2, 0), Eccentricity = `3/2`


Find the vertex, focus, equation of directrix and length of the latus rectum of the following:

y2 = 16x


Find the vertex, focus, equation of directrix and length of the latus rectum of the following:

x2 = 24y


Find the vertex, focus, equation of directrix and length of the latus rectum of the following:

y2 = – 8x


Prove that the length of the latus rectum of the hyperbola `x^2/"a"^2 - y^2/"b"^2` = 1 is `(2"b"^2)/"a"`


Show that the absolute value of difference of the focal distances of any point P on the hyperbola is the length of its transverse axis


Identify the type of conic and find centre, foci, vertices, and directrices of the following:

`(x - 3)^2/225 + (y - 4)^2/289` = 1


Identify the type of conic and find centre, foci, vertices, and directrices of the following:

`(x + 3)^2/225 + (y - 4)^2/64` = 1


Identify the type of conic and find centre, foci, vertices, and directrices of the following:

`(y - 2)^3/25 + (x + 1)^2/16` = 1


Identify the type of conic and find centre, foci, vertices, and directrices of the following:

18x2 + 12y2 – 144x + 48y + 120 = 0


Choose the correct alternative:

If P(x, y) be any point on 16x2 + 25y2 = 400 with foci F(3, 0) then PF1 + PF2 is


Choose the correct alternative:

If x + y = k is a normal to the parabola y2 = 12x, then the value of k is 14


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×