For Exercises 41–50, write the standard form of the equation of the hyperbola subject to the given conditions. (See Example 5)
Vertices:
Foci:
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
College Algebra (Collegiate Math)
- Write conic section in standard formarrow_forwardFind a or k so that the points (-5,-8) and (1,-25) lie on the parabola y=a(x+3)²+karrow_forwardFor Exercises 27–34, an equation of a parabola x = 4py or y = 4px is given. a. Identify the vertex, value of p, focus, and focal diameter of the parabola. b. Identify the endpoints of the latus rectum. c. Graph the parabola. d. Write equations for the directrix and axis of symmetry. (See Examples 2-3) 27. x -4y 28. x -20y 29. 10y = 80x 30. 3y = 12x 31. 4x 40y 32. 2x 14y 33. y = 34. y = -2x = -X %3Darrow_forward
- What is the vertex of the parabola y = (x+3)²-4? A B с D (3,4) (-3,4) (-3,-4) (3,-4)arrow_forward3) Explain how changing the a, h, and k variables affect the shape of the parabola in the vertex form y = a(x - h)² + k. [3 Communication Marks] Page 1arrow_forwardWhich parabola has a vertex at the (0, 3) and opens to the right? O y=x²+3 O y = -(x + 3)² Ox=y²-3 O x = (y - 3)² O-(x+3)² = (y - 3)²arrow_forward
- Consider the parabola y = -3x2+42x-150. What is the vertex (-7,-3) (-7,3) (7,-3) (7,3)arrow_forward11arrow_forward2. Suppose that the last three digits of your student number are like. abc . It is not important whether it is a 4 digit number or a 5 digit number, take the last three :+(-1) ; (b+1)3 digits as abc. Consider the conic (-1)ª following. Major semiaxis Minor semiaxis (-1)ab. Find the %3D (a+1)a i. ii. iii. Vertices iv. Foci Eccentricity Directrices Asymptotes (if it is a hyperbola) and the graph (geogebra or nice handmade) V. vi. vii. Now, consider the Quadratic Surface (-1)ª. (a+1)a +(-1) + (-1)° (b+1) =(-1)abe. (c+1)2 Find the following. Name of the surface viii. ix. Traces of the surface Nice Graph (in GeoGebra or handmade) х. For example, your professor's ID number is 0000005121. So, he will study the conic (-1) + (-1) =(-1)*2 which gives (-) + (-1)', (1+1) = (-1)12 which gives (-) + = 1. Also he will (2+1)3 4 study the quadratic surface (-1)' (1+1)2 + (-1)² - (2+1)a + (-1)'; :(-1)121 (1+1) which gives. (-) + + (-÷) = 1.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage