Day 1 Notes Circles April 21, 2014

Conic Sections

Conic SectionsMM3G2

Circle: the set of all points that are equidistant from a fixed point called the center.

The distance from any point on the circle to the center is called the radius.

The Standard Form of a circle with center (h,k) and radius r:

The Standard Form of a circle with center (0,0) and radius r:

EX: Write in SF. Find the center and radius and then graph.

1) x2 = 25 - y2

Day 1 Notes Circles April 21, 2014

2) (x-2)2 + (y+1)2 = 9 3) 6x2 + 6y2 = 48

4) (x + 3)2 + (y - 5)2 = 18 Given the following information, write the standard form for the circle.

a) r = 8, center (3, -2)

b) D = 22, center (0, 0)

5)

r = radius D = diameter

Day 1 Notes Circles April 21, 2014

c) r = 9/25, center (-4, -5)

d) D =3/4 center (-6, 0)

e)  center:  (0, 9)   r = 3√5

6)

*** What 2 things do we need to know to write the equation of a circle? What are we missing?

HELPS to sketch graph!!

The point (6,2) lies on a circle whose center is the origin. Write the standard form of the circle.

The point (3, 0) lies on a circle whose center is (1, -1). Write the standard form of the circle.

7)

Reminder:  

In Math 2 we learned that where a tangent of a circle is perpendicular to the radius of the circle.

Day 1 Notes Circles April 21, 2014

In 8th grade, we learned that lines that are perpendicular have slope that are the negative reciprocal to each other.

Which means if the slopeof one line is...   then the other line's slope is...

m = 9 perp. m =

m = ­ 3/4 perp. m =

m = 1 perp. m = 

Also we learn that the equation of a line is...

y ­ y1 = m (x ­ x1)

Reminder:

Finding the equation of the line tangent to the circle

Steps:  1)   Use given point on circle  (aka point of tangency) and the center to find the slope between these 2 points.  

Find slope using one of 2 methods...a)  graph the 2 pts and do 

b)  Use Slope Formula

2)  Formulate the slope of the tangent line by finding the negative reciprocal of the slope in 

step 1.  (flip and change signs of previous slope)

3)  Using the point on circle ( x1, y1) and perp. slope  (   m), plug info into the equation of  a line formula

y ­ y1  =   m(x ­ x1)

4)  Solve for y.  

When you get y = mx + b, this is the equation of the line tangent to the circle at the given point.

T

(T)

8) Write the equation of a line tangent to the circle x2 + y2 = 10 at (-1, 3). Write the equation of a line tangent to

the circle (x + 3)2 + (y - 5)2 = 13 at (0,3).9)