What are the focus and directrix of the parabola with the given equation x=-1/8y^2

1 answer:

7 0

X=-1/8y^2
If the Vertex is at the origin: V=(h,k)=(0,0)→h=0, k=0
y^2=4px

(-8)(x=-1/8y^2)
-8x=y^2
y^2=-8x

4p=-8
Solving for p:
4p/4=-8/4
p=-2<0 (negative)→The parabola opens to the left

Focus: F=(p,0)→F=(-2,0)
Drectrix: x=-p=-(-2)→Directrix: x=2

Answers:
Focus=(-2,0)
Directrix: x=2

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$\text{Let the side of square 1, square 2 and square 3 be x, y and z respectively.}\\\\\text{Given that,}\\\\\text{Perimeter of square 1,~~ p =100 units.}\\\\\text{So}~ x=\dfrac p 4 = \dfrac{100}4 =25~\text{units.}\\\\\\\text{Area of square 2, a = 225 units}^2\\\\\text{So}~y = \sqrt{a} = \sqrt {225} = 15~ \text{units.}\\\\\text{Use Pythagorean theorem to find z}^2\\\\x^2 =y^2 +z^2 \\\\\implies 25^2 = 15^2 +z^2\\\\\implies z^2 = 625 - 225 = 400\\\\\\$