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MTH-5105 Pretest A

8. r = 4. -8. 2. -2. MTH-5105 Pretest A. Represent graphically: x 2 – 6x + y 2 – 2y + 1 ≤ 0. Determine the equation of the circle below in general form. What is the equation of the tangent to the circle with equation (x – 1) 2 + (y – 2) 2 = 5 with point of tangency (2,0)?.

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MTH-5105 Pretest A

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  1. 8 r = 4 -8 2 -2 MTH-5105 Pretest A • Represent graphically: • x2 – 6x + y2 – 2y + 1 ≤ 0 • Determine the equation of the circle below in general form.

  2. What is the equation of the tangent to the circle with equation (x – 1)2 + (y – 2)2 = 5 with point of tangency (2,0)? • Represent graphically and indicate the vertex, focus, axis of symmetry and directrix.

  3. x = -3 F (-3,0) V (-3,-1) y = -2 • Determine the equation of the parabola below in its standard form. • Represent the following inequality on a cartesian plane. Give the coordinates and indicate on the graph of the vertices and the foci and draw and state the asymptotes.

  4. C (-5,-3) • Give the domain and range of this relation. Use either set-builder or interval notation.

  5. 6 10 (0,3) -5 5 12 -12 (-5,0) (5,0) (0,-3) -10 -6 • Determine the expression for the 2 relations below. Express them in standard form.

  6. Determine the equation of the circle in its general form, given that its centre is and its radius is 4 units. C(2,3) (1,y1) (3,y2) • Find the equation of the parabola inscribed in a circle with centre (2,3) and whose radius is equal to 2. The abscissa of the vertex is 2. We know also that the parabola intersects the circle at abscissas 1 and 3.

  7. d { cosmos • The elliptical sign of “cosmos” restaurant measures 4 meters in length and 2 meters in width. The owner wants to attach the sign above the O’s. The sign has a width of 1.6 meters at those points. How far apart will the attachments be separated.

  8. 1 m 9 m 2 m 16 m ? • Christian wants to hit his golf ball onto the green (area with the flag). This green is elevated 2 meters from the current position of his golf ball which lies 16 meters in front of a tree that is 9 meters high. When he hits the ball, it reaches a maximum height 1 meter directly over the tree. Knowing that the ball follows a parabolic trajectory, what horizontal distance does the ball travel when it strikes the green.

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