Practice

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Automatic translation, not reviewed, of the Hebrew lesson your child follows at school.

עשרה תרגילים על כל הפרק, מהקל לקשה.

Exercises

Exercise 1

מהו שיעור ה-xx של המוקד של y2=20xy^2 = 20x?

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Answer: 5

Worked solution:

p=10p = 10

55.

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Exercise 2

מהי משוואת המדריך של x2=−4yx^2 = -4y?

  1. y=1y = 1
  2. x=1x = 1
  3. y=−1y = -1
  4. y=2y = 2
Show the answer and the solution

Answer: A y=1y = 1

Worked solution:

p=2 ; נפתחת למטהp = 2 \ ; \ \text{נפתחת למטה}

y=1y = 1.

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Exercise 3

PP על y2=6xy^2 = 6x, ו-x0=2x_0 = 2. חשבו את PFPF.

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Answer: 3.5

Worked solution:

2+1.52 + 1.5

3.53.5.

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Exercise 4

מהו שיפוע המשיק ל-y2=6xy^2 = 6x בנקודה (6,6)(6, 6)?

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Answer: 0.5

Worked solution:

6y=3(x+6)6y = 3(x + 6)

12\frac{1}{2}.

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Exercise 5

הישר y=x+ky = x + k משיק ל-y2=12xy^2 = 12x. מהו kk?

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Answer: 3

Worked solution:

k=p2m=62\begin{aligned}k &= \tfrac{p}{2m} \\ &= \tfrac{6}{2}\end{aligned}

33.

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Exercise 6

הישר y=−x+1y = -x + 1 חותך את y2=4xy^2 = 4x בשתי נקודות.

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Answer: True

Worked solution:

x2−6x+1=0 ; Δ=32\begin{aligned}x^2 - 6x + 1 &= 0 \ ; \ \Delta \\ &= 32\end{aligned}

נכון.

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Exercise 7

חשבו את אורך המיתר שהישר x=4x = 4 חותך מ-y2=4xy^2 = 4x.

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Answer: 8

Worked solution:

y=±4y = \pm 4

88.

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Exercise 8

הפרבולה y2=2pxy^2 = 2px עוברת בנקודה (3,6)(3, 6). מהו pp?

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Answer: 6

Worked solution:

36=6p36 = 6p

66.

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Exercise 9

מהו המקום הגאומטרי של הנקודות שמרחקן מ-(−2,0)(-2, 0) שווה למרחקן מהישר x=2x = 2?

  1. y2=−8xy^2 = -8x
  2. y2=−4xy^2 = -4x
  3. x2=−8yx^2 = -8y
  4. y2=8xy^2 = 8x
Show the answer and the solution

Answer: A y2=−8xy^2 = -8x

Worked solution:

(x+2)2+y2=(x−2)2(x + 2)^2 + y^2 = (x - 2)^2

y2=−8xy^2 = -8x.

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Exercise 10

המשיק ל-y2=8xy^2 = 8x בנקודה (8,8)(8, 8) חותך את ציר ה-xx. באיזה שיעור xx?

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Answer: -8

Worked solution:

(−x0, 0)(-x_0,\ 0)

−8-8.

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