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nika2105 [10]
2 years ago
9

NO LINKS!! Please help me with this problem​

Mathematics
2 answers:
vova2212 [387]2 years ago
6 0

{\qquad\qquad\huge\underline{{\sf Answer}}}

The given vertex and Focus are of a vertical parabola having an opening downward as the focus is in downward direction as the vertex.

Focus of the parabola can be written as :

\qquad \sf  \dashrightarrow \: (h ,k+ a )

where, h and k are coordinates of vertex

so,

  • k + a = -2

  • -1 + a = -2

  • a = -1

So, the equation of parabola can be written as :

\qquad \sf  \dashrightarrow \: (x - h) {}^{2}  = 4a(y - k)

plug in the values ~

\qquad \sf  \dashrightarrow \: (x - 1) {}^{2}  =  4(- 1)(y  + 1) {}^{}

\qquad \sf  \dashrightarrow \: (x - 1) {}^{2}  =  - 4(y + 1)

Brilliant_brown [7]2 years ago
6 0

Answer:

(x-1)^2=-4(y+1)

Step-by-step explanation:

<u />

<u>Standard form of a parabola with a vertical axis of symmetr</u>y:

(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0

  • Vertex = (h, k)
  • Focus = (h, k+p)
  • Directrix: y = (k-p)
  • Axis of symmetry: h = k
  • If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.

Given:

  • vertex = (1, -1)
  • focus = (1, -2)

Comparing with the formulas:

⇒ h = 1

⇒ k = -1

⇒ k + p = -2  ⇒ -1 + p = -2  ⇒ p = -1

Substituting the values into the formula:

\implies (x-1)^2=4(-1)(y-(-1))

\implies (x-1)^2=-4(y+1)

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