Question

Find the equation of parabola if the curve is open leftward, vertere is (2, 1) and passing through the point (6,3)​

Answer 1

The parabola's equation is x²-4x-8y+10 when the vertex is (2, 1) and going through the spot if the curve is open leftward (6,3) .

Given that,

We have to find the parabola's equation. The vertex is (2, 1) and going through the spot if the curve is open leftward (6,3) .

We know that,

The equation of parabola if the curve is open leftward then

(x-h)² = 4a(y-k)

Here,

(x,y) = (6,3) and (h,k) =(2,1)

So,

(6-2)² = 4a(3-1)

4² =4a(2)

16 = 8a

a = $\frac{16}{8}$

a= 2

Then,

(x-2)² = 4×2(y-1)

x²-4x+4 =8(y-1)

x²-4x+4=8y-8

x²-4x-8y+4+8=0

x²-4x-8y+10

Therefore, The parabola's equation is x²-4x-8y+10 when the vertex is (2, 1) and going through the spot if the curve is open leftward (6,3) .

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