Question

find the equation of parabola whose focus
is (0, -3) and vertex is (-1, -3)​

Answer 1

EXPLANATION.

Equation of parabola whose focus is ( 0,-3)  and  vertex is = ( -1,-3).

It is in the form of ⇒ x² = -4by.

By using the focus and vertex we can find b.

Distance Formula = √(x₁ - x₂)² + ( y₁ - y₂)².

Let x₁ = 0  and y₁ = -3.

Let x₂ = -1  and  y₂ = -3.

⇒ √(0 - (-1))² + ( -3 - (-3))²

⇒ √ (1)² + 0² = 1.

⇒ b = 1.

(a) = Vertex = ( 0,0).

Vertex = ( x - (-1) = ( x + 1 )

Vertex = ( y - (-3)) = ( y + 3 ).

Equation of parabola = ( x + 1)² = -4.1.(y + 3 ).

Equation of parabola = ( x + 1)² = -4( y + 3).

                                                           

MORE INFORMATION.

EQUATION OF CHORD.

(1) = The equation of chord joining the points P (x₁, y₁) and Q (x₂, y₂) on the parabola y² = 4ax is,

⇒ y ( y₁ + y₂) = 4ax + y₁y₂.

(2) = The equation of chord joining P ( at₁², 2at₁) and Q ( at₂², 2at₂) is,

⇒ y ( t₁ + t₂) = 2 ( x + at₁t₂).