What is the y-intercept in the equation 2y = x -8

2. Consider the circle x² + y2 = 1, given in figure. Let OP makes an angle 30° with the x axis.

PolarNik [594]

The equation of the tangent line to the circle passing through the point P is; y = (1/√3)x ± 2/√3

<h3>How to find the equation of the tangent?</h3>

I) We are given the equation of the circle as;

x² + y² = 1

Since angle of inclination is 30°, then slope is;

m = tan 30 = 1/√3

Then equation of the tangent will be;

y = (1/√3)x + c

Put (√3)x + c into the given circle equation to get;

x² + ((1/√3)x + c)² = 1

x² + ¹/₃x² + (2/√3)cx + c² = 1

⁴/₃x² + (2/√3)x + (c² - 1) = 0

Since we need to find value of c for equation to become tangent, then the above quadratic equation must have real and equal roots.

Thus;

((2/√3)c)² - 4(⁴/₃)(c² - 1) = 0

⁴/₃c² - ¹⁶/₃(c² - 1) = 0

⁴/₃c² - ¹⁶/₃c² + ¹⁶/₃ = 0

4c² = ¹⁶/₃

c² = ⁴/₃

c = √⁴/₃

c = ±²/√3

Thus, equation of tangent is;

y = (1/√3)x ± 2/√3

II) Radius from the given equation is 1. Thus, we will use trigonometric ratio to find the x and y intercept;

x-intercept is at y = 0;

0 = (1/√3)x ± 2/√3

-(1/√3)x = ±2/√3

Intercept is positive. Thus;

x = (2/√3)/(1/√3)

x = 1

y - intercept is positive at x = 0;

y = (1/√3)0 ± 2/√3

y = 2/√3

Read more about Equation of tangent at; brainly.com/question/17040970

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6 0

1 year ago

A retangular field is 18 yards in length and 51 feet in width. what is the area in square yards

Scrat [10]

Answer:

2754

Step-by-step explanation:

Given,

Length = 18 yards is equivalent to 54 feet

Width = 51 feet

So area of the field = Length * width

= 54 x 51

=2754 square feet

4 0

3 years ago

Determine the graph of the polar equation r =6/2-2cos theta<br> (picture provided)

vredina [299]

Answer:

Choice D is correct

Step-by-step explanation:

The first step is to write the polar equation of the conic section in standard form by dividing both the numerator and the denominator by 2;

$r=\frac{3}{1-cos(theta)}$

The eccentricity of this conic section is thus 1, the coefficient of cos θ. Thus, this conic section is a parabola since its eccentricity is 1.

The value of the directrix is determined as;

d = k/e = 3/1 = 3

The denominator of the polar equation of this conic section contains (-cos θ) which implies that this parabola opens towards the right and thus the equation of its directrix is;

x = -3

Thus, the polar equation represents a parabola that opens towards the right with a directrix located at x = -3. Choice D fits this criteria

5 0

3 years ago

A video game system and several games are sold for $500. The cost of the game is 3 times as much as the cost of the system . Fin

Shalnov [3]

We have to start by creating an equation.

Cost of System = x
Cost of games = 3x

Thus x + 3x = $500

Now we find x.

4x = 500,
x = 500/4 = 125

So the system is 125,
The games, 125*3 = 375

5 0

3 years ago

Read 2 more answers

Write an equation for a line parallel to the line y=1/3x-4 through (3,-2)

Sphinxa [80]

Answer:

is it for a test or something

Step-by-step explanation:

5 0

2 years ago