The Circle and Ellipse Answers

1.a
 x2 + y2 = 25
b
 x2 + y2 = 9
c
 (x − 2)2 + (y − 1)2 = 25
d
 (x − 7)2 + (y − 3)2 = 16
e
 (x + 3)2 + (y − 2)2 = 4
f
 (x − 5)2 + (y + 1)2 = 100
g
 (x − 3)2 + y2 = 9
h
 x2 + (y + 2)2 = 36

 

2. a
 (0, 0); 9
b
 (0, 0); 11
c
 (2, 3); 4
d
 (5, 4); 3
e
 (-1, 6); 5
f
 (-3, -1); 7
g
 (-7, 0); 8
h
 (0, 4); 4

 

3. a
 (-1, -3); 5
b
 (-4, -5); 7
c
 (5, 4); 7
d
 (3, -3); 5
e
 (-6, 1); 7
f
 (3, -4); 5
g
 (2, 2); 1
h
 (-2.5, 1.5); 2.915

4.

a.

b.

c.

d.

5. c. -1
d. (7, 7)
e. 1
f. y = x
g. The perpendicular bisector of a chord is a diameter.

6. c. 7y = x + 25
d. (-0.5, 3.5)
e. (0, 0)
f. y = -7x
h. A diameter passes through the mid-point of a chord at 90°.

7. b. A (0, 0), B(6, 0)
e. √2/ 2, -√ 2
f. Angle in a semi-circle is 90°

8. b. (-6, 0)
d. 4 / 3
e. -4 /(x0 + 3)
f. x0 = 7 / 3
g. PQ is a tangent.
h. OP = 5, PQ = 20 / 3., OQ = 25 / 3...
i. tangent meets radius at 90°