CBSE - Class 11 Mathematics Conic Sections Worksheet
1.
In each of the following Exercises 1 to 6, find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. 4. $x^2$ = – 16$y$
2.
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions: 12. Vertices (± 6, 0), foci (± 4, 0)
3.
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions: 11. Vertices (0, ± 13), foci (0, ± 5)
4.
Find the centre and radius of the circles. 9. 2$x^2$ + 2$y^2$ – $x$ = 0
5.
Does the point (–2.5, 3.5) lie inside, outside or on the circle $x^2$ + $y^2$ = 25?
6.
In each of the Exercises 7 to 15, find the equations of the hyperbola satisfying the given conditions. 10. Foci (± 5, 0), the transverse axis is of length 8.
7.
In each of the following Exercises 1 to 6, find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. 2. $x^2$ = 6$y$
8.
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions: 10. Vertices (± 5, 0), foci (± 4, 0)
9.
The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.
10.
In each of the following Exercises 1 to 6, find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. 1. $y^2$ = 12$x$
11.
In each of the Exercises 7 to 12, find the equation of the parabola that satisfies the given conditions: 8. Focus (0,–3); directrix $y$ = 3
12.
In each of the Exercises 1 to 6, find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas. 5. 5$y^2$ – 9$x^2$ = 36
13.
Find the equation of the circle with radius 5 whose centre lies on $x$-axis and passes through the point (2,3).
14.
Find the centre and radius of the circles. 6. ($x$ + 5)$^2$ + ($y$ – 3)$^2$ = 36
15.
In each of the Exercises 7 to 12, find the equation of the parabola that satisfies the given conditions: 9. Vertex (0,0); focus (3,0)
16.
In each of the Exercises 1 to 9, find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse. 1. $frac{x^2}{36} + $frac{y^2}{16} = 1$
17.
In each of the Exercises 7 to 15, find the equations of the hyperbola satisfying the given conditions. 14. vertices (± 7,0), $e$ = $frac{4}{3}$.
18.
In each of the following Exercises 1 to 6, find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. 6. $x^2$ = – 9$y$
19.
A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the $x$-axis.
20.
In each of the Exercises 7 to 12, find the equation of the parabola that satisfies the given conditions: 12. Vertex (0,0), passing through (5,2) and symmetric with respect to $y$-axis.
