Using a directrix of y = −2 and a focus

zachutnat4o

zachutnat4o

Answered question

2021-11-16

Using a directrix of y = −2 and a focus of (2, 6), what quadratic function is created?
f(x)=(x2)22
f(x)=(x2)2+2
f(x)=(x2)22
of f(x)=(x+2)22

Answer & Explanation

Florence Pittman

Florence Pittman

Beginner2021-11-17Added 15 answers

To find equation of quadratic function
Given, directrix, y= -2
And focus= (2, 6)
We know, from any point (x, y) on the parabola the focus and directrix are equidistant
1. Distance of(x, y) from (2, 6)= distance of directrix, y= -2 from (x, y)
((x2)2+(y6)2)0.5=|y(2)| {using distance formula, if (x1,y1) and (x2,y2) are two points then dist between them is ((x1x2)2+(y1y2)2)0.5}
((x2)2+(y6)2)0.5=|y+2|
Squaring both sides, we get
(((x2)2+(y6)2)0.5)2=(|y+2|)2
(x2)2+(y6)2=(y+2)2
(y6)2(y+2)2=(x2)2
Y2+3612y(y2+4+4y)=(x2)2
Y2+3612yy244y=(x2)2
16y+32=(x2)2
(x2)2+32=16y
16y=(x2)2+32
Y=116(x2)2+3216
Y=116(x2)2+2
Hence, the quadratic function is
F(x)=116(x2)2+2

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