Answer:
<h2>a) 17</h2>Step-by-step explanation:
<em>Look at the picture.</em>
We have the right triangle (red). Use the Pythagorean theorem:
We have
Substitute:
<em>use (a - b)² = a² - 2ab + b²</em>
<em>subtract r² from both sides</em>
<em>subtract 306 from both sides</em>
<em>divide both sides by (-18)</em>
Answer:
y = - 2x + 13
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (5, 3) and (x₂, y₂ ) = (4, 5)
m = =
= - 2, thus
y = - 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (4, 5), then
5 = - 8 + c ⇒ c = 5 + 8 = 13
y = - 2x + 13 ← equation of line
Answer:
The equation of a parabola is
Step-by-step explanation:
(h,k) is the vertex and (f,k) is the focus.
Thus, f = 1, k = −4.
The distance from the focus to the vertex is equal to the distance from the vertex to the directrix: f - h = h - 2.
Solving the system, we get h = 3/2, k = -4, f = 1.
The standard form is:
The general form is:
The vertex form is:
The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus: y = -4.
The focal length is the distance between the focus and the vertex: 1/2.
The focal parameter is the distance between the focus and the directrix: 1.
The latus rectum is parallel to the directrix and passes through the focus: x = 1.
The length of the latus rectum is four times the distance between the vertex and the focus: 2.
The eccentricity of a parabola is always 1.
The x-intercepts can be found by setting y = 0 in the equation and solving for x.
x-intercept:
The y-intercepts can be found by setting x = 0 in the equation and solving for y.
y-intercepts: