ME PODRIAN AYUDAR CON ESTA TAREA?

SolucióN

1) ( x + 5)² / 81 + ( y - 3 )² / 100 = 1 elipse centro : C = ( - 5 , 3 ) = (h, k) a² = 100 a = 10 b² = 81 b = 9 c² = a² - b² = 100 - 81 = 19 c = √19 vértices : A1 = ( h , k + a ) = ( - 5 , 3 + 10 ) = ( - 5 , 13 ) A2 = ( h , k - a ) = ( - 5, 3 - 10) = ( - 5 , - 7) B1 = ( h + b , k ) = ( - 5 + 9, 3 ) = ( 4, 3 ) B2 = ( h - b , k) = ( - 5 - 9 , 3 ) = ( - 14 , 3 ) longitud del eje menor = 2 * a = 2 * 10 = 20 longitud del eje mayor = 2 * b = 2 * 9 = 18 2) 9x² + 4y² - 36x - 8y + 4 = 0 9x² - 36x + 4y² - 8y = - 4 9 * ( x² - 4x + 4 ) + 4 * ( y² - 2y + 1 ) = - 4 + 36 + 4 9 * ( x - 2)² + 4 * ( y - 1 )² = 36 ÷36 ( x - 2 )² / 4 + ( y - 1 )² / 9 = 1 Centro = C = ( h , k) = ( 2 , 1 ) a² = 9 a = 3 b² = 4 = b = 2 a² = b² + c² c = √( a² - b²) = √( 9 - 4 ) = √5 3 ) 6y² - 12x = 0 6y² = 12x y² = 12x / 6 y² = 2x ecuación reducida V( 0, 0) h = 0 k = 0 y² = 4py 4p = 2 p = 1 / 2 foco = ( h + p, k) = ( 1 / 2 , 0) directriz = x = - p / 2 = x = - 1 / 4 4) ( y + 3 )² = 16 * ( x + 5 ) Vértice = V = ( h, k ) = ( - 5 , - 3 ) longitud de lado recto = Lr = I 4 * p I = I 4 * 4 I = 16 .