Find the standard form of the equation of the hyperbola satisfying the given con

Question

Find the standard form of the equation of the hyperbola satisfying the given conditions. 21) Fod: (,-9), (o, 9); vertices: (0,-6), (0, 6) 21)_ 36 45-1 36 81 36 81 36 45 Find the standard form of the equation of the parabola using the information given. 22) Focus: (-4,0% Directrix: y4 A) (2)2-8(y 4) C) (y 2)2-8(x+4) B)42-8y+2) D) (y 4)2-8(x 2) Identify the equation without completing the square. 25)y2-iczho ay D) ellpe 23) A) hyperbola C) circle D) parabola Identify the equation without applying a rotation of axes 24) x2+ 4xy 4y2 2x-3y-4- 24) A) circle B) parabola C) ellipse D) hyperbola Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric equations. 25) 25) x -2t-1, y 2+6-4sts4 A)y-x21 2sxs2 o)y-2.1, -6sxs4 11 25 Identify the conic section that the polar equation represents. Describe the location of a directrix from the focus located the pole. 26)r-1-3 sin 6 26) A) hyperbola; The directrix is 3 unit(s) to the left of the pole atx--3. B) hyperbola; The directrix is 3 unit(s) above the pole at y-3 C) hyperbola; The directrix is 3 unit(s) to the right of the pole at x 3. D) hyperbola; The directrix is 3 unit(s) below the pole at y -3. A-4

Explanation / Answer

21) foci = (0,-9) (0,9)

vertices (0,6) , (0,-6)

a = 6 , c = 9

b = sqrt ( 9^2 - 6^2 ) = sqrt 45

hence, equation is

y^2 / 36 - x^2/45 = 1

option a is correct

22) focus = ( - 4,0) , directrix y = -4

so, vertex = ( -4 , -2 )

hence, we can write the equation as

8(y+2) = ( x + 4)^2

option b is correct

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