हिंदी

Find the equation of the following parabolas: Directrix x = 0, focus at (6, 0) - Mathematics

Advertisements
Advertisements

प्रश्न

Find the equation of the following parabolas:

Directrix x = 0, focus at (6, 0)

योग

उत्तर

Given that directrix = 0 and focus (6, 0)

∴ The equation of the parabola is (x – 6)2 + y2 = x2

⇒ x2 + 36 – 12x + y2 = x2

⇒ y2 – 12x + 36 = 0

Hence, the required equations is y2 – 12x + 36 = 0

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 11: Conic Sections - Exercise [पृष्ठ २०३]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
अध्याय 11 Conic Sections
Exercise | Q 28.(a) | पृष्ठ २०३

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum.

y2 = – 8x


Find the equation of the parabola that satisfies the following condition:

Focus (6, 0); directrix x = –6


Find the equation of the parabola that satisfies the following condition:

Focus (0, –3); directrix y = 3


Find the equation of the parabola that satisfies the following condition:

Vertex (0, 0) passing through (2, 3) and axis is along x-axis


Find the equation of the parabola that satisfies the following condition:

Vertex (0, 0), passing through (5, 2) and symmetric with respect to y-axis.


If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.


An equilateral triangle is inscribed in the parabola y2 = 4 ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.


Find the equation of the parabola whose: 

focus is (3, 0) and the directrix is 3x + 4y = 1


Find the equation of the parabola whose focus is the point (2, 3) and directrix is the line x − 4y + 3 = 0. Also, find the length of its latus-rectum.

 


Find the equation of the parabola if 

 the focus is at (−6, −6) and the vertex is at (−2, 2)


Find the equation of the parabola if the focus is at (a, 0) and the vertex is at (a', 0) 


At what point of the parabola x2 = 9y is the abscissa three times that of ordinate? 


Find the equation of the parabola whose focus is (5, 2) and having vertex at (3, 2). 


If the line y = mx + 1 is tangent to the parabola y2 = 4x, then find the value of m


The equation of the parabola whose vertex is (a, 0) and the directrix has the equation y = 3a, is 


The parametric equations of a parabola are x = t2 + 1, y = 2t + 1. The cartesian equation of its directrix is 


The line 2x − y + 4 = 0 cuts the parabola y2 = 8x in P and Q. The mid-point of PQ is


If the coordinates of the vertex and the focus of a parabola are (−1, 1) and (2, 3) respectively, then the equation of its directrix is 


If V and S are respectively the vertex and focus of the parabola y2 + 6y + 2x + 5 = 0, then SV


Find the length of the line segment joining the vertex of the parabola y2 = 4ax and a point on the parabola where the line segment makes an angle θ to the x-axis.


Find the equation of the following parabolas:

Focus at (–1, –2), directrix x – 2y + 3 = 0


Find the equation of the set of all points the sum of whose distances from the points (3, 0) and (9, 0) is 12.


The line lx + my + n = 0 will touch the parabola y2 = 4ax if ln = am2.


The equation of the parabola having focus at (–1, –2) and the directrix x – 2y + 3 = 0 is ______.


If the focus of a parabola is (0, –3) and its directrix is y = 3, then its equation is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×