Sketch the following conic sections:a) y^2-4y+8-4x^2=8 b)y^2-4y-4x^2=8 c)3(y-5)^2-7(x+1)^2=1

Maiclubk 2021-08-07 Answered
Sketch the following conic sections:
a)y24y+84x2=8
b)y24y4x2=8
c)3(y5)27(x+1)2=1
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Expert Answer

Nichole Watt
Answered 2021-08-08 Author has 100 answers
Answered 2021-12-13

a) 

Solve for y:
y24y4x2+8=0

Hint: Solve the quadratic equation by completing the square.
Subtract 4x2+8 from both sides:
y24y=4x28

Hint: Take one half of the coefficient of y and square it, then add it to both sides.
Add 4 to both sides:
y24y+4=4x24

Hint: Factor the left hand side.
Write the left hand side as a square:
(y2)2=4x24

Hint: Eliminate the exponent on the left hand side.
Take the square root of both sides:
y2=4x24ory2=4x24

Hint: Look at the first equation: Solve for y.
Add 2 to both sides:
y=4x24+2ory2=4x24

Hint: Look at the second equation: Solve for y.
Add 2 to both sides:
Answer: y=4x24+2ory=24x24

b) 

Solve for y:
y24y4x2=8

Hint: Solve the quadratic equation by completing the square.
Add 4x2 to both sides:
y24y=4x2+8

Hint: Take one half of the coefficient of y and square it, then add it to both sides.
Add 4 to both sides:
y24y+4=4x2+12

Hint: Factor the left hand side.
Write the left hand side as a square:
(y2)2=4x2+12

Hint: Eliminate the exponent on the left hand side.
Take the square root of both sides:
y2=4x2+12ory2=4x2+12

Hint: Look at the first equation: Solve for y.
Add 2 to both sides:
y=4x2+12+2ory2=4x2+12

Hint: Look at the second equation: Solve for y.
Add 2 to both sides:
Answer: y=4x2+12+2ory=24x2+12

c) 

Solve for y:
3(y5)27(x+1)2=1

Hint: Isolate terms with y to the left hand side.
Add 7(x+1)2 to both sides:
3(y5)2=7(x+1)2+1

Hint: Divide both sides by a constant to simplify the equation.
Divide both sides by 3:
(y5)2=73(x+1)2+13

Hint: Eliminate the exponent on the left hand side.
Take the square root of both sides:
y5=73(x+1)2+13ory5=73(x+1)2+13

Hint: | Look at the first equation: Solve for y.
Add 5 to both sides:

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