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Second Year Math Conic Sections


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1.Findanequationofthehyperbolawiththegivendata.Sketchthegraphofeach.(ii)Foci(±50)vertex(30)1. Find an equation of the hyperbola with the given data. Sketch the graph of each.(ii) Foci (\pm 50) vertex (30)

Example 2. Discuss and sketch the graph of the equation\[25 x^{2}-16 y^{2}=400\]
Example 2. Discuss and sketch the graph of the equation\[25 x^{2}-16 y^{2}=400\]

Example 2. Discuss and sketch the graph of the equation\[25 x^{2}-16 y^{2}=400\]

8. Find the points of intersection of the given conics(ii) x^{2}+y^{2}=8 and x^{2}-y^{2}=1
8. Find the points of intersection of the given conics(ii)  x^{2}+y^{2}=8   and   x^{2}-y^{2}=1

8.Findthepointsofintersectionofthegivenconics(ii)x2+y2=8andx2y2=18. Find the points of intersection of the given conics(ii) x^{2}+y^{2}=8 and x^{2}-y^{2}=1

2. Find the centre and radius of the circle with the given equation(d) 4 x^{2}+4 y^{2}-8 x+12 y-25=0
2. Find the centre and radius of the circle with the given equation(d)  4 x^{2}+4 y^{2}-8 x+12 y-25=0

2.Findthecentreandradiusofthecirclewiththegivenequation(d)4x2+4y28x+12y25=02. Find the centre and radius of the circle with the given equation(d) 4 x^{2}+4 y^{2}-8 x+12 y-25=0

3. Write an equation of the circle that passes through the given points (a) A(45) B(-4-3) C(8-3)
3. Write an equation of the circle that passes through the given points (a)  A(45) B(-4-3) C(8-3)

3.Writeanequationofthecirclethatpassesthroughthegivenpoints(a)A(45)B(43)C(83)3. Write an equation of the circle that passes through the given points (a) A(45) B(-4-3) C(8-3)

1. Find an equation of the ellipse with given data and sketch its graph:(iv) Vertices (-11)(51) ; foci (41) and (01)
1. Find an equation of the ellipse with given data and sketch its graph:(iv) Vertices  (-11)(51) ; foci  (41)  and  (01)

1.Findanequationoftheellipsewithgivendataandsketchitsgraph:(iv)Vertices(11)(51);foci(41)and(01)1. Find an equation of the ellipse with given data and sketch its graph:(iv) Vertices (-11)(51) ; foci (41) and (01)

1. Find an equation of the hyperbola with the given data. Sketch the graph of each.(ii) Foci (\pm 50) vertex (30)
1. Find an equation of the hyperbola with the given data. Sketch the graph of each.(ii) Foci  (\pm 50)  vertex  (30)
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1.Findanequationofthehyperbolawiththegivendata.Sketchthegraphofeach.(ii)Foci(±50)vertex(30)1. Find an equation of the hyperbola with the given data. Sketch the graph of each.(ii) Foci (\pm 50) vertex (30)

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