Distance and Midpoint Formulas; Circles Flashcards
What’s the Pythagorean theorem?
The hypothenuse squared is equal to the sum of the squares of the sides.
What’s the Pythagorean formula?
c^2 = a^2 + b^2.
To what type of triangle only does the Pythagorean theorem apply?
The Pythagorean theorem applies only to right triangles.
What theorem helps find the distance between two points on a cartesian plane?
The Pythagorean theorem.
What’s the standard form of the distance formula?
d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2), where d is the distance.
What’s the midpoint formula?
((x_2 + x_1)/2, (y_2 + y_1)/2)
What’s the definition of a circle?
A circle is the set of all points in a plane that are equidistant from a fixed point, called the center. The fixed distance from the circle’s center to any point on the circle is called the radius.
How is the coordinate of the center of a circle often denoted?
(h,k).
How is the radius of a circle found, and what information is needed to accomplish that?
By using the distance formula. The information needed is a random point on the circle and the circle’s center.
What’s the general form of the equation of a circle?
x^2 + y^2 + Dx + Ey + F = 0, where D, E, and F are real numbers.
How is the general form of the equation of a circle transformed into standard form?
By completing the square for x and y:
(x^2 + Dx + (D/2)^2) + (y^2 + Ey + (E/2)^2) = -F + (D/2)^2 + (E/2)^2.
Can the equation of circle be the equation of a function?
No.
Write the standard form of the equation of the circle with the given center and radius:
Center (3,2), r = 5.
(x - 3)^2 + (y - 2)^2 = 25.
