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La longitud de la cuerda que se forma al interceptar la parábola y²- 4x = 0 con la recta x -2y +3 = 0 es de 8. 94 unidades de longitud. Explicación paso a paso: Inicialmente debemos buscar la intersección entre la recta y la parábola, para ello igualamos las funciones, tal que: y² - 4x = 0 → x = y²/4 x -2y + 3 = 0 → x = 2y - 3 Igualamos y tenemos que: y²/4 = 2y -3 y²/4 -2y + 3 = 0 Aplicamos resolvente tenemos que: y₁ = 6 y₂ = 2 Buscamos el valor de la coordenada -x-: x₁ = 6²/4 = 9 x₂ = 2²/4 = 1 Por tanto, la recta corta a la parábola en los puntos A(9, 6) y B(1, 2). Ahora, buscamos la distancia entre estos puntos: d = √[(x₁-x₂)² + (y₁-y₂)²] d = √[(9-1)² + (6-2)²] d = 8. 94 Por tanto, la longitud de la cuerda que se forma al interceptar la parábola y²- 4x = 0 con la recta x -2y +3 = 0 es de 8. Comprueba esta respuesta en.
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