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

חשבו את המרחק מ-(1,2)(1, 2) לישר 3x−4y+15=03x - 4y + 15 = 0.

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Answer: 2

Worked solution:

∣3−8+15∣5\frac{|3 - 8 + 15|}{5}

22.

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Exercise 2

מהם המרכז והרדיוס של x2+y2−4x+6y−12=0x^2 + y^2 - 4x + 6y - 12 = 0?

  1. (2, −3)(2,\ -3), 12\sqrt{12}
  2. (4, −6)(4,\ -6), 55
  3. (−2, 3)(-2,\ 3), 55
  4. (2, −3)(2,\ -3), 55
Show the answer and the solution

Answer: D (2, −3)(2,\ -3), 55

Worked solution:

(x−2)2+(y+3)2=12+4+9(x - 2)^2 + (y + 3)^2 = 12 + 4 + 9

(2,−3)(2, -3), 55.

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Exercise 3

המשיק ל-x2+y2=25x^2 + y^2 = 25 בנקודה (3,4)(3, 4) חותך את ציר ה-yy. באיזה שיעור yy?

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Answer: 6.25

Worked solution:

3x+4y=253x + 4y = 25
x=0⇒y=254\begin{aligned}x &= 0 \Rightarrow y \\ &= \tfrac{25}{4}\end{aligned}

6.256.25.

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Exercise 4

הישר y=x+ky = x + k, k>0k > 0, משיק ל-x2+y2=8x^2 + y^2 = 8. מהו kk?

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Answer: 4

Worked solution:

∣k∣2=8\frac{|k|}{\sqrt 2} = \sqrt 8

k=4k = 4.

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Exercise 5

הנקודה (6,1)(6, 1) מחוץ למעגל (x−2)2+(y−1)2=9(x - 2)^2 + (y - 1)^2 = 9.

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Answer: True

Worked solution:

16>916 > 9

נכון.

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Exercise 6

בכמה נקודות הישר y=2x+1y = 2x + 1 חותך את x2+y2=1x^2 + y^2 = 1?

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Answer: 2

Worked solution:

d=15<1d = \frac{1}{\sqrt 5} < 1

22.

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Exercise 7

מה המצב ההדדי של x2+y2=1x^2 + y^2 = 1 ו-(x−3)2+y2=4(x - 3)^2 + y^2 = 4?

  1. זרים
  2. נחתכים
  3. משיקים מבפנים
  4. משיקים מבחוץ
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Answer: D משיקים מבחוץ

Worked solution:

d=3=1+2\begin{aligned}d &= 3 \\ &= 1 + 2\end{aligned}

משיקים מבחוץ.

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Exercise 8

A(0,0)A(0, 0), B(0,6)B(0, 6). המקום הגאומטרי PA=PBPA = PB הוא ישר y=cy = c. מהו cc?

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Answer: 3

Worked solution:

x2+y2=x2+(y−6)2x^2 + y^2 = x^2 + (y - 6)^2

33.

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Exercise 9

A(1,1)A(1, 1), B(7,9)B(7, 9). המקום הגאומטרי ∠APB=90∘\angle APB = 90^\circ הוא מעגל. מהו הרדיוס שלו?

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Answer: 5

Worked solution:

AB=36+64=10\begin{aligned}AB &= \sqrt{36 + 64} \\ &= 10\end{aligned}

55.

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Exercise 10

חשבו את אורך המיתר שהישר y=3y = 3 חותך מ-x2+y2=25x^2 + y^2 = 25.

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Answer: 8

Worked solution:

x2=16⇒x=±4\begin{aligned}x^2 &= 16 \Rightarrow x \\ &= \pm 4\end{aligned}

88.

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