Podcast
Questions and Answers
What is the equation of a circle with its center at (3, -4) and a radius of 5 units?
What is the equation of a circle with its center at (3, -4) and a radius of 5 units?
- $(x-3)^2 + (y+4)^2 = 25$ (correct)
- $(x+3)^2 + (y-4)^2 = 25$
- $(x-3)^2 + (y+4)^2 = 5$
- $(x+3)^2 + (y-4)^2 = 5$
If the point (5, -2) lies on the circle $x^2 + y^2 - 6x + 4y - 12 = 0$, what is the center of the circle?
If the point (5, -2) lies on the circle $x^2 + y^2 - 6x + 4y - 12 = 0$, what is the center of the circle?
- (6, 4)
- (3, 2)
- (3, -2) (correct)
- (6, -4)
What is the equation of a line that passes through the points (1, 3) and (4, 7)?
What is the equation of a line that passes through the points (1, 3) and (4, 7)?
- $y = \frac{4}{3}x + \frac{1}{3}$
- $y = \frac{3}{4}x - \frac{1}{4}$
- $y = \frac{4}{3}x - \frac{1}{3}$ (correct)
- $y = \frac{3}{4}x + \frac{1}{4}$
If the circles $x^2 + y^2 - 6x + 4y - 12 = 0$ and $(x-9)^2 + (y-7)^2 = 25$ intersect at two distinct points, what is the distance between their centers?
If the circles $x^2 + y^2 - 6x + 4y - 12 = 0$ and $(x-9)^2 + (y-7)^2 = 25$ intersect at two distinct points, what is the distance between their centers?
Flashcards
Circle Equation
Circle Equation
The equation of a circle with center (h, k) and radius r is (x - h)² + (y - k)² = r²
Circle Point
Circle Point
A point lies on a circle if it satisfies the circle's equation.
Line Equation
Line Equation
The equation of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by y - y₁ = m(x - x₁), where m = (y₂ - y₁) / (x₂ - x₁).
Circle Centers
Circle Centers
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