Question

The equation y2 – 4y – 4x + 16 = 0 represents a parabola. Find its vertex and
focus.

Answer 1

Answer:

hi

Step-by-step explanation:

the answer is in the attachment

Answer 2

The equation of the parabola is

y² – 4y – 4x + 16 = 0.

Or, (y – 2)² = 4x – 12.

Or, (y – 2² = 4(x – 3).

Let Y² = 4x, where, Y = y – 2 and X = x – 3.

Here 4a = 4 => a = 1.

Therefore, vertex is V (0, 0).

$\\ \texttt{When Y = 0 => y – 2 = 0, or, y = 2.}$

$\texttt{When X = 0 => x – 3 = 0 , or, x = 3.}$

Therefore, vertex is V (3, 2).

Focus is F(a, 0) = F(1, 0).

$\\ \texttt{Or, X = a = 1 => x – 3 = 1 => x = 4 and Y = 0 => y – 2 = 0 => y = 2.}$

Therefore, focus is F(4, 2).

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