TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT Given Conic Equation9x² - 4y² +54x +16y +29 = 09x² - 4y² + 54x + 1by = -29Complete the square for 9x²+54xfoome 92²+bx+c to find.Use thea, b, and ca=96=54Consider the vertex form of parabolaa(x+d)² + eFind the valueda b292542x9b2पवValueCHOof d using the=Find the value of e using the formulaеe= c-20-(54)2value of e9(2+3)²-81= -814x9Subtitute the values of a, dande inthe vertexof d = 5/20₁b291/22Subtitute 9(2+3)²-81 for 9x² +54xin the equationto find the value of9x² - 4y² +54x + 16y=-299(2+3) ²2²-81-4y² + 16y = -9 (x+3)² - 4y²+1by9(x+3)² - 4y² +1byC=O= C-= 3Complete the Square for _4y² +167Use the form ax²+bx+c, to find the value of a, band ca = - 4b=16Consider the vertex form of parabolaG (a+d)² + e=e formula5249162X (-4)= -2=-29+8)= +62(16)2= 164 X (-4)Subtitute the value of a, d ande into the vertexform-4(y-2)² +16Subtitute -4 (9-2)² +16 for - 4y² +16y in the equation.Gx² - 4y² + 54x+16y=-299 (x+3)² - 4(y + 2)² + 16 = -29+8| 9 (x+3)² - 4(4+2)²9(2+3)² -4(y+2)² = 36divide each term by 36 to make theright side equal to one.9 (x+3)²36(2+3)²41(x-4)²924(५+2)236(y-2)29This is the form of a hyperbola.Standrad form of hyperbolo(Y-K 2²b2= -29 +81-16Here, a=2, b= 3, K=2, h=-3The center of hyperbola (hik)(-3,2)Find the distance from the center to a focus

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TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT Given Conic Equation9x² - 4y² +54x +16y +29 = 09x² - 4y² + 54x + 1by = -29Complete the square for 9x²+54xfoome 92²+bx+c to find.Use thea, b, and ca=96=54Consider the vertex form of parabolaa(x+d)² + eFind the valueda b292542x9b2पवValueCHOof d using the=Find the value of e using the formulaеe= c-20-(54)2value of e9(2+3)²-81= -814x9Subtitute the values of a, dande inthe vertexof d = 5/20₁b291/22Subtitute 9(2+3)²-81 for 9x² +54xin the equationto find the value of9x² - 4y² +54x + 16y=-299(2+3) ²2²-81-4y² + 16y = -9 (x+3)² - 4y²+1by9(x+3)² - 4y² +1byC=O= C-= 3Complete the Square for _4y² +167Use the form ax²+bx+c, to find the value of a, band ca = - 4b=16Consider the vertex form of parabolaG (a+d)² + e=e formula5249162X (-4)= -2=-29+8)= +62(16)2= 164 X (-4)Subtitute the value of a, d ande into the vertexform-4(y-2)² +16Subtitute -4 (9-2)² +16 for - 4y² +16y in the equation.Gx² - 4y² + 54x+16y=-299 (x+3)² - 4(y + 2)² + 16 = -29+8| 9 (x+3)² - 4(4+2)²9(2+3)² -4(y+2)² = 36divide each term by 36 to make theright side equal to one.9 (x+3)²36(2+3)²41(x-4)²924(५+2)236(y-2)29This is the form of a hyperbola.Standrad form of hyperbolo(Y-K 2²b2= -29 +81-16Here, a=2, b= 3, K=2, h=-3The center of hyperbola (hik)(-3,2)Find the distance from the center to a focus<= √6²45²= √(²)² + (3)² = √√4+9 =√13Find the eccentricityeccentricity =Find the focal parameterFocal Parameter36= 1Find the verticesThe first vertex of a hyperbola can be found byadding a to h(h+a, k)(-1,2)19²+52= 1The second vestex of a hyperbola can be by foundby Subtracting a from h(n-a, k)36(-5,2)The vertices of a hyperbola (-1,2), (-5,2)Find the fociThe first focus of a hyperbola can be found byadding (toh(h+(₂ k)(-3+√√13,2)Seond second focus of a hyperbolafound by Subtracting c from h(h-C, K) (-3-√√13, 2)The foci of a hyperbola (-3+√73, 2) (-3-√73,2)First Asymptotesy = 3x + 1322Second Asymptatesy = ± 3 (x-(-3)+22√√/2²+32262=32√a²+5²113Asymptotes follow the form y: I bla-h)+because this hyperbola open left and rightay=-321-57/2can be2=9/1313+K

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Introduction:
One of the key concepts in geometry is conic sections. The angle generated between the…

Given Conic Equation 2 9x² - 44² +548 +164 +29