मराठी
तामिळनाडू बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान इयत्ता १२

Find the vertex, focus, equation of directrix and length of the latus rectum of the following: y2 = 16x - Mathematics

Advertisements
Advertisements

प्रश्न

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

y2 = 16x

बेरीज
Advertisements

उत्तर


4a = 16

a = 4

(a) Vertex V(0, 0)

(b) Focus S(a, 0) = S(4, 0)

(c) Equation of the directrix x = – a

x = – 4

⇒ x + 4 = 0

(d) Length of the latus rectum = 4a

= 4(4)

= 16

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Two Dimensional Analytical Geometry-II - Exercise 5.2 [पृष्ठ १९७]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
पाठ 5 Two Dimensional Analytical Geometry-II
Exercise 5.2 | Q 4. (i) | पृष्ठ १९७

संबंधित प्रश्‍न

Find the equation of the parabola whose focus is the point F(-1, -2) and the directrix is the line 4x – 3y + 2 = 0.


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

y2 = 20x


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

x2 = - 16y


The average variable cost of the monthly output of x tonnes of a firm producing a valuable metal is ₹ `1/5`x2 – 6x + 100. Show that the average variable cost curve is a parabola. Also, find the output and the average cost at the vertex of the parabola.


The eccentricity of the parabola is:


The distance between directrix and focus of a parabola y2 = 4ax is:


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

Focus (4, 0) and directrix x = – 4


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:

Centre (2, 1), one of the foci (8, 1) and corresponding directrix x = 4


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:

x2 – 2x + 8y + 17 = 0


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


Choose the correct alternative:

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


Which statement best describes a focal chord in any conic section?


If the eccentricity e > 1, the conic section is:


A chord passing through any point on the conic and perpendicular to the axis is called:


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×