Q1. Find the vertex, focus, axis, and directrix of the following
= 0.
Q2. Find a , b , and c of the ellipse
+
parabola: x2 - 4x - 8y + 28
=1
Q3. What is the eccentricity of the ellipse 81x
2
+y
2
- 324x - 6y + 252 = 0 ?
Q4. Is the transverse axis of this hyperbola horizontal or vertical: -
+
= 1.
Q5. The eccentricity of a hyperbola with center (0, 0) and focus 5, 0) is
standard equation for the hyperbola?
. What is the
Q6. Find the vertex, focus, axis, and directrix of the following parabola: x2 - 10x - 2y + 29
= 0.
Q7. What is the center and radius of the circle x
Q8. Find the vertices of the ellipse 2x
2
+3y
2
2
+y
2
- 8x - 16y + 60 = 0 ?
-6=0
Q9. Find the point of intersection.
4x2 + y2 + 40x – 28y + 40 = 0
4x2 + y2 + 72x – 28y + 456 = 0
Q10. Sketch the graph of the equation.
–16x2 + 9y2 + 64x+ 144y+496 =0
Q11. A circle with equation (x – 120)2 + (y – 150)2 = 19600 is given. Expand and simplify
the binomials in this equation in order to get an equation of the form
Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 and find the values of A, B,C, D, E, and F.
Q12. find the equation of the parabola with vertical axis and passing through (-2,3),(0,3)
and (1,9)
Q13. find the equation of the hyperbola with foci (0,±3) and vertices (0,±1)
Q14. find the equation of the ellipse with center (2,2),focus(0,2) and vertex (5,2)
Q15-17. Given the following equation
9x2 - 16y2 = 144
15) Find the x and y intercepts, if possible, of the graph of the equation.
16) Find the coordinates of the foci.
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17) Sketch the graph of the equation.
Q18. Find the points of intersection of the two hyperbolas given by their equations as
follows:
Q19 Identify the conic and find its characteristics:
(y – 5)2 = 4(5)(x – 3)
Q20. Write the new equation obtained by translating the equation
2 units right and 4 units up.
ANSWERS:A1. Vertex: (2, 3) . Focus: (2, 5) . Axis: x = 2 .
Directrix: y = 1 .
A2. a = 3,b=
,c=
A3. a = 9 , b = 1 , and c =
A4. Because the y
A5.
-
2
Therefore, e = =
term is negative, the transverse axis is horizontal.
=1.
A6. Vertex: (5, 2) . Focus: (5, 2.5) . Axis: x = 5 . Directrix: y = 1.5 .
A7. Center: (4, 8) radius
A8.
and
A9. (–13, 14)
A10. Given equation is hyperbola with center (2, –8) and a = 4, b = 3
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A11. A = 1, B = 0, C = 1, D = –240, E = –300 and F = 17,300
A12.
A13.
A14.
A15. X intercept 8 unit ,y intercept 0(not cutting)
A16. The foci are F1(5,0) and F2 (-5 , 0)
A17.
A18. (-3.83 , 6.53);( -3.83,-6.53)
A19. Parabola with vertex (3,5)
A20.
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