Question

1. Describe, sketch and label the focus, vertex and directrix of the parabola
16x2 + 24x – 32y + 25 = 0.​

Answer 1

Answer:

bajakklajnnjakjnnjkanjkkkNbnnK

Step-by-step explanation:

KhaionanjajakNNjkkoankookann

Answer 2

SOLUTION

TO DETERMINE

Describe, sketch and label the focus, vertex and directrix of the parabola

$\sf{16 {x}^{2} + 24x - 32y + 25 = 0 }$

EVALUATION

Here the given equation of the parabola is

$\sf{16 {x}^{2} + 24x - 32y + 25 = 0 }$

$\displaystyle\sf{ \implies {(4x)}^{2} + 2 \times 4x \times 3 + {(3)}^{2} - 32y + 16 = 0 }$

$\displaystyle\sf{ \implies {(4x + 3)}^{2} = 32y - 16 }$

$\displaystyle\sf{ \implies { \bigg(x + \frac{3}{4} \bigg)}^{2} = 2 \bigg(y - \frac{1}{2} \bigg) }$

Comparing with

$\displaystyle\sf{ \implies { \bigg(x - \alpha \bigg)}^{2} = 4a \bigg(y - \beta \bigg) }$

We get

$\displaystyle\sf{ \implies \alpha = - \frac{3}{4} \: , \: a = \frac{1}{2} \: ,\: \beta = \frac{1}{2} }$

$\displaystyle\sf{ focus = ( \alpha \: , \: a + \beta ) = \bigg( - \frac{3}{4} ,1 \bigg) }$

$\displaystyle\sf{ vertex = ( \alpha \: , \: \beta ) = \bigg( - \frac{3}{4} \: , \: \frac{1}{2} \bigg) }$

Equation of the directrix

$\sf{y + a = \beta }$

$\displaystyle\sf{ \implies \: y + \frac{1}{2} = \frac{1}{2} }$

$\displaystyle\sf{ \implies \: y = 0 }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. Find the centre, the length of axes, eccentricity, foci of the ellipse 3x2 + 4y2 -12x – 8y +4 =0

https://brainly.in/question/25777605

2. If base radius of a cylinder is doubled then the volume of new cylinder = ______times the volume of given cylinder

https://brainly.in/question/33235561