What is the point-slope form of a line with slope -3 that contains the point (10, -1)?

1 answer:

4 0

When in point-slope form, the number next to the y and the x by themselves will be the opposite of what they would actually be as coordinates. This means that the y-coordinate, -1, will show up as y+1. This eliminates A and B out of the choices.

The slope is -3, which will be the number outside of the parentheses, which is what we see in C’s answer or -3(x-10).

Therefore, the answer is C: y+1 = -3(x-10).

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1:Under what condition will the line px+py+r=0 mat be a normal to the circke x²+y²+2gx+2fy+c=0

ahrayia [7]

Answer:

The normal overlaps with the diameter, so it passes through the center.

Let's find the center of the circle:

x² + y² + 2gx + 2fy + c = 0
(x + g)² + (y + f)² = c + g² + f²

The center is:

(-g, -f)

Since the line passes through (-g, -f) the equation of the line becomes:

p(-g) + p(-f) + r = 0
r = p(g + f)

This is the required condition

Rewrite equations and find centers and radius of both circles.

Circle 1

x² + y² + 2ax + c² = 0
(x + a)² + y² = a² - c²
The center is (-a, 0) and radius is √(a² - c²)

Circle 2

x² + y² + 2by + c² = 0
x² + (y + b)² = b² - c²
The center is (0, -b) and radius is √(b² - c²)

The distance between two centers is same as sum of the radius of them:

d = √(a² + b²)

Sum of radiuses:

√(a² - c²) + √(b² - c²)

Since they are same we have:

√(a² + b²) = √(a² - c²) + √(b² - c²)

Square both sides:

a² + b² = a² - c² + b² - c² + 2√(a² - c²)(b² - c²)
2c² = 2√(a² - c²)(b² - c²)

Square both sides:

c⁴ = (a² - c²)(b² - c²)
c⁴ = a²b² - a²c² - b²c² + c⁴
a²c² + b²c² = a²b²

Divide both sides by a²b²c²:

1/a² + 1/b² = 1/c²

Proved

6 0

3 years ago

Read 2 more answers

jim ran 15.2 miles over the weekend . he ran 6.75 miles on saturday. how many miles did he run on sunday?

kap26 [50]

Subtract 6.75 from 15.2 to find what he did on Sunday, because supposed the number of miles he ran on Sunday was x. Therefore, the formula should be x + 6.75 = 15.2
Solve that, and you should get that Jim ran 8.45 miles on Sunday.

8 0

3 years ago

[[3+ (8-3^2)-2] +3] / 5-2•2

katovenus [111]