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**Formulas and definitions of circle **

**formula and definitions of ellipse**

**formula and definition of hyperola **

**In each of the following Exercises 1 to 4, find the equation of the circle with
1. centre (0,2) and radius 2 ...**

**find the equation of the circle with . centre (–a, –b) and radius root (a2 - b2)
**

**9.find the centre and radius of the circles 2x 2 + 2y – x = 0 2**

**10. Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre is on the line 4x + y = 16.
**

**12. Find the equation of the circle with radius 5 whose centre lies on x-axis and
passes through the point (2,3).
**

**13. Find the equation of the circle passing through (0,0) and making intercepts a and b on the coordinate axes.
**

**14. Find the equation of a circle with centre (2,2) and passes through the point (4,5).
**

**15. Does the point (–2.5, 3.5) lie inside, outside or on the circle x2 + y2 = 25?**

**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.**

**In each of the Exercises 7 to 12, find the equation of the parabola that satisfies the given conditions:
7. Focus (6,0); directrix x = – 6 8. Focus (0,–3); directrix y = 3
9. Vertex (0,0); focus (3,0) 10. Vertex (0,0); focus (–2,0)**

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

**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.**

**10. Find the equation for the ellipse whose vertex and foci are given Vertices (± 5, 0), foci (± 4, 0) **

**13. Ends of major axis (± 3, 0), ends of minor axis (0, ± 2) find the equation for the ellipse that satisfies
the given conditions**

**14. Ends of major axis (0, ±), ends of minor axis (± 1, 0) find the equation for the ellipse that satisfies
the given conditions
**

**15. Length of major axis 26, foci (± 5, 0)
find the equation for the ellipse that satisfies
the given conditions:
**

**17. Foci (± 3, 0), a = 4find the equation for the ellipse that satisfies
the given conditions:
**

**18. b = 3, c = 4, centre at the origin; foci on a x axis.**

**20 . Major axis on the x-axis and passes through the points (4,3) and (6,2).
**

**Q 1- 6 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.**

**Q 7 - 11. In each of the Exercises 7 to 15, find the equations of the hyperbola satisfying the given conditions.
Vertices (± 2, 0), foci (± 3, 0)**

**Q 12 - 13 Foci (± 3, 0), the latus rectum is of length 8. 13. Foci (± 4, 0), the latus rectum is of length 12
5
**

**14. vertices (± 7,0), e = .
15. Foci (0, ± 10), passing through (2,3)**

**Example 17 The focus of a parabolic mirror as shown in Fig 11.33 is at a distance of
5 cm from its vertex. If the mirror is 45 cm deep, find
**

**Ex - 18 A beam is supported at its ends by2 Fig 11.33 supports which are 12 metres apart. Since the load is concentrated at its centre, there is a deflection of 3 cm at the centre and the deflected beam is in the shape of a
parabola. How far from the centre is the deflection 1 cm?**

**Example 19 A rod AB of length 15 cm rests in between two coordinate axes in such
a way that the end point A lies on x-axis and end point B lies on
y-axis. A point P(x, y) is taken on the rod in such a way
that AP = 6 cm. Show that the locus of P is an ellipse.**

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

**2. An arch is in the form of a parabola with its axis vertical. The arch is 10 m high
and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?
**

**3. 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.
**

**4. An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre.
Find the height of the arch at a point 1.5 m from one end.
**

**5. 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.**

**6. Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latus rectum.
**

**7. A man running a racecourse notes that the sum of the distances from the two flag
posts from him is always 10 m and the distance between the flag posts is 8 m.
Find the equation of the posts traced by the man.**

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

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