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slega [8]
3 years ago
9

Derive the equation of the parabola with a focus at (–5, 5) and a directrix of y = -1.

Mathematics
2 answers:
Elza [17]3 years ago
6 0
( x + 5 )^2 = - ( y - 5 )
Dvinal [7]3 years ago
4 0

Answer:

(x+5)^2=12(y-2)

Step-by-step explanation:

We are given that focus of parabola at (-5,5).

Equation of directrix y=-1

We have to derive the equation of parabola

We know that the parabola is the set of points (x,y) equally distant from (-5,5) and (x,-1).

Distance formula

\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Apply this formula

\sqrt{(x+5)^2+(y-5)^2}=\sqrt{(x-x)^2+(y+1)^2}

Squaring on both sides then we get

(x+5)^2+(y-5)^2=(y+1)^2

(x+5)^2+y^2-10y+25=y^2+2y+1  ((a-b)^2=a^2+b^2-2ab,(a+b)^2=a^2+b^2+2ab)

(x+5)^2=y^2+2y+1-y^2+10y-25

(x+5)^2=12y-24

(x+5)^2=12(y-2)

This is required equation of parabola along y- axis.

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Mr. Smith had 34 of a peach pie left over. He split the leftover pie among his 3 co-workers.
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8 0
3 years ago
At the gym, Jasper was able to bench press 224 pounds, which was 7/8 of the weight that Balin was able to bench press. Which sho
Rzqust [24]

Answer:

The answer SHOULD be 7/8=224/x;256 pounds.

You may have made a mistake in inputting it here on Brainly. So look for the one that matches that.

Step-by-step explanation:

This is what we know:

Jasper = 224 pounds

Balin = x

Jasper = 7/8 of x

Now we make an equation for that:

(\dfrac{7}{8})(x) = 224pounds

To match the selections we will isolate 7/8 on one side of the equation:

\dfrac{7}{8}=\dfrac{224}{x}

Using ratio and proportion we can solve for what x is. Multiply 224 by 8 and divide it by 7. Or you can do it this way too:

\dfrac{7}{8}=\dfrac{224}{x}

(7)(x)=(224pounds)(8)

7x=1792pounds

x=\dfrac{1792pounds}{7}=256pounds

So x = 256 pounds

7 0
2 years ago
Read 2 more answers
Need help with this question
photoshop1234 [79]
y = 3/4 x + ( - 2)
4 0
2 years ago
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How would you divide 5.6 into five even pieces
stealth61 [152]
U do 5.6/5; that would get you to 1.12. so 5.6/5=.12. that;s ur answer
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3 years ago
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