Download Answer Sheet 20: Conics

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Answer Sheet 20: Conics
Sketch the following curves:
Equation
1) (𝑥 − 2)2 + (y − 2)2 = 9
Sketch
𝑦
(2, 2)
𝑥 and 𝑦 terms both squared and added.
Coefficient of 𝑥 2 and 𝑦 2 are equal.
No 𝑥𝑦 term.
x
𝑥
∴ it’s a circle.
Radius = 3
2)
(𝑥 − 4)2 + (y + 5)2 = 36
𝑦
Radius = 6
𝑥 and 𝑦 terms both squared and added.
Coefficient of 𝑥 2 and 𝑦 2 are equal.
No 𝑥𝑦 term.
𝑥
∴ it’s a circle.
3)
(𝑥 + 3)2 + (y + 1)2 = 16
𝑦
𝑥 and 𝑦 terms both squared and added.
Coefficient of 𝑥 2 and 𝑦 2 are equal.
No 𝑥𝑦 term.
Radius = 4
𝑥
x
(−3, −1)
∴ it’s a circle.
4)
(4, −5)
x
𝑥 2 + y 2 = 100
𝑦
Radius = 10
10
𝑥 and 𝑦 terms both squared and added.
Coefficient of 𝑥 2 and 𝑦 2 are equal.
No 𝑥𝑦 term.
-10
10
𝑥
∴ it’s a circle.
-10
5)
𝑥2
16
+
𝑦2
36
𝑦
=1
6
𝑥 and 𝑦 terms both squared and added.
Coefficient of 𝑥 2 and 𝑦 2 are not equal.
∴ it’s an ellipse.
4
−4
−6
© H Jackson 2011 / ACADEMIC SKILLS
𝑥
6)
𝑥2
25
+
𝑦2
4
=1
𝑦
𝑥 and 𝑦 terms both squared and added.
Coefficient of 𝑥 2 and 𝑦 2 are not equal.
∴ it’s an ellipse.
2
−5
𝑥
5
−2
7)
9𝑥 2 + 4𝑦 2 = 36
𝑦
𝑥 and 𝑦 terms both squared and added.
Coefficient of 𝑥 2 and 𝑦 2 are not equal.
∴ it’s an ellipse.
3
𝑥
2
−2
−3
8)
𝑥2
16
−
𝑦2
9
=1
𝑦
𝑥 and 𝑦 terms both squared and subtracted.
3
∴ it’s a hyperbola.
9)
𝑥2
9
−
𝑦2
4
=1
4
𝑥
𝑦
𝑥 and 𝑦 terms both squared and subtracted.
2
3
∴ it’s a hyperbola.
10) 98𝑥 2 − 50𝑦 2 = 2450
𝑥 and 𝑦 terms both squared and subtracted.
∴ it’s a hyperbola.
𝑥
𝑦
7
5
𝑥
© H Jackson 2011 / ACADEMIC SKILLS