In This Post we are providing Chapter- 11 CONIC SECTIONS NCERT MOST IMPORTANT QUESTIONS for Class 11 MATHS which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.
NCERT MOST IMPORTANT QUESTIONS CONIC SECTIONS
1.Find the equation of an ellipse whose foci are & the eccentricity is ?
Ans. Let the required equation of the ellipse be
let the foci be &
Now
Hence equation is
2.Find the equation of an ellipse whose vertices are &
Ans. Let equation be
& its vertices are
Let
Then
Now
Hence the equation is
3.Find the equation of hyperbola whose length of latus rectum is 36 & foci are
Ans. Clearly C = 12
Length of cat us rectum
Now
This
Hence,
4.Find the equation of a circle drawn on the diagonal of the rectangle as its diameter, whose sides are
Ans. Let ABCD be the given rectangle &
Then
So the equation of the circle with AC as diameter is given as
5.Find the coordinates of the focus & vertex, the equations of the diretrix & the axis & length of latus rectum of the parabola
Ans.
&
So,
So it is case of downward parabola
o, foci is
Its vertex is
So,
Its axis is y – axis, whose equation is length of lotus centum
units.
6.Show that the equation represents a circle. Also find its centre & radius.
Ans.
So
Where,
Hence, centre of circle &
Radius of circle
units
7.Find the equation of the parabola with focus at & directrix is
Ans.Focus lies to the right hand side of the origin
So, it is right hand parabola.
Let the required equation be
So,
8.Find the equation of the hyperbola with centre at the origin, length of the transverse axis 18 & one focus at (0,4)
Ans.Let its equation be
Clearly, C = 4.
length of the transverse axis
Also,
So,
So, equation is
9.Find the equation of an ellipse whose vertices are the foci are
Ans.Let the equation be
& a = 13
Let its foci be then
So,
So, equation be
10.Find the equation of the ellipse whose foci are & length of whose major axis is 10
Ans. Let the required equation be
Let
Its foci are
Also, a = length of the semi- major axis =
Now,
Then,
Hence the required equation is
11.Find the equation of the hyperbola with centre at the origin, length of the transverse axis 8 & one focus at (0,6)
Ans. Let its equation by
Clearly, C = 6
& length of the transverse axis
Also,
So,
Hence, the required equation is
12.Find the equation of the hyperbola whose foci are at & the length of whose conjugate axis is
Ans. Let it equation be
Let it foci be
Length of conjugate axis
Also,
Hence, required equation is
13.Find the equation of the hyperbola whose vertices are & foci are
Ans. The vertices are
But it is given that the vertices are
Let its foci be
But it is given that the foci are
Now
Then
Hence the required equation is
14.Find the equation of the ellipse for which & whose vertices are
Ans. Its vertices are therefore a =10
Let
Then,
Now,
Hence the required equation is
15.Find the equation of the ellipse, the ends of whose major axis are & the ends of whose minor axis are
Ans. Its vertices are & therefore, a = 5 ends of the minor axis are
i.e length of minor axis = 25 units
Now,
Hence, the required equation