A curve is traced by a point P(x, y) which moves such that its distance from the point A(-1,1) is three times its distance from the point B(2,-1). Determine the equation of the curve.

Answers

Answer 1

Answer:

Answer:

$8x^2+8y^2+43-38x+20y=0$

Step-by-step explanation:

Let $A\left ( x_1,y_1 \right )$ and $B\left ( x_2,y_2 \right )$ be two points then distance AB is equal to $AB=√(\left ( x_2-x_1 \right )^2+\left ( y_2-y_1 \right )^2)$

Here, a curve is traced by a point $P(x,y)$ which moves such that its distance from the point $A(-1,1)$ is three times its distance from the point $B(2,-1)$ i.e $AP=3BP$

Using distance formula,

$AP=√((-1-x)^2+(1-y)^2)$

$BP=√((2-x)^2+(-1-y)^2)$

$AP=3BP\n√((-1-x)^2+(1-y)^2)=3√((2-x)^2+(-1-y)^2)$

On squaring both sides, we get

$(-1-x)^2+(1-y)^2=9\left [ (2-x)^2+(-1-y)^2 \right ]\n1+x^2+2x+1+y^2-2y=9\left ( 4 +x^2-4x+1+y^2+2y\right )\n1+x^2+2x+1+y^2-2y=36+9x^2-36x+9+9y^2+18y\n8x^2+8y^2+43-38x+20y=0$

So, equation of curve is $8x^2+8y^2+43-38x+20y=0$

Related Questions

Someone please help me . )):
PLEASE SOMEONE HELP ME!!!!!!!!
The radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters. A cone is used to fill the cylinder with water. The radius of the cone's base is 5 centimeters, and its height is 10 centimeters.The number of times one needs to use the completely filled cone to completely fill the cylinder with water is
The center of a circle is at (7, –3) and it has a radius of 9. What is the equation of the circle?(x – 7)2 + (y + 3)2 = 3 (x + 7)2 + (y – 3)2 = 3 (x + 7)2 + (y – 3)2 = 81 (x – 7)2 + (y + 3)2 = 81
Solve, using the substitution method.4x + 2y = 11x – 2 = – 2yA.B.C.D.

Convert
4
5
to a percent (Review question)

Answers

Answer:

45%?

Step-by-step explanation:

If the answer is wrong lack of info was provided

Answer:

4/5 into a decimal is 0.8.

You can find the answer to any fraction conversion into a decimal. By simply dividing the fraction 4/5=0.8

What is 6a squared - 12a+36

Answers

6a²-12a+36= 6a²-12a=-36
Put the normal number on the other side to have the variables on one side, and the normal number on the other.
Then group:
= 36a-12a= -36
= 24a=-36
Then isolate a:
= a=-36/24
Then simplify:
=a = - 3/2

Hope this helps!

6a² - 12a + 36 = 0
a = -(-12) +/- √((-12)² - 4(6)(36))
      2(6)
a = 12 +/- √(144 - 864)
      12
a = 12 +/- -√720
   12
a = 12 +/- -√(9 × 16 × 5)
   12
a = 12 +/- -√9 -√16 -√5
   12
a = 12 +/- (-3)(-4) -√5
   12
a = 12 +/- 12-√5
      12
a = 12 +/- 12(-2.236067978)
      12
a = 12 +/- (-26.83281573)
   12
a = 12 + (-26.83281573) a = 12 - (26.83281573)
      12       12
a = 12 - 26.83281573 a = 12 + 26.83281573
   12 12
a = -14.83281573 a = 38.832815723
   12 12
-1.236067978 a = 3.236067978

Which is greater 8 quarts or 16 pints?

Answers

They're equal because 1 quart = 2 pints.

Graham and Hunter are circus performers. A cable lifts Graham into the air at a constant speed of 1.5 ft/s. When Graham’s arms are 18 ft above the ground, Hunter, who is standing directly underneath Graham, throws Graham a ball as the cable continues to lift him higher. Hunter throws the ball from a position 5 ft above the ground with an initial velocity of 24 ft/s. Which system of equations can be used to model this situation?A) h=18+1.5t
h=5+24t-16t^2

B) h=18+1.5t
h=5+24t+16t^2

C) h=18+1.5t
h=5+24t

D) h=18t+1.5t-16t^2
h=5+24t-16t^2

Answers

Answer: Hello there!

this type of equations in one dimension (when all the factors are constants) are written as:

h = initial position + initial velocity*t + (acceleration/2)*t^2

First, let's describe the hunter's equation:

We know that Graham moves with a velocity of 1.5 ft/s, and when he is 18 ft above the ground, Hunter throws the ball, and because Graham is pulled with a cable, he is not affected by gravity.

If we define t= 0 when Graham is 18 ft above the ground, the equation for Graham height (in feet) is:

h = 18 + 1.5t

where t in seconds.

Now, the equation for the ball:

We know that at t= 0, the ball is thrown from an initial distance of 5ft, with an initial velocity of 24ft/s and is affected by gravity acceleration g, where g is equal to: 32.2 ft/s (notice that the gravity pulls the ball downwards, so it will have a negative sign)

the equation for the ball is:

h = 5 + 24t - (32.2/2)t^2 = 5 + 24t - 16.1t^2

So the system is:

h = 18 + 1.5t

h = 5 +24t - 16.1t^2

so the right answer is A

Answer:

Step-by-step explanation:

EDGE 2020

Solve the equation and check your answer.
(that is one fifth )
1/5t-3=-17

Answers

$(1)/(5) t$ - 3 = -17

First, simplify $(1)/(5) t$ to $(t)/(5)$ / Your problem should look like: $(t)/(5) - 3 = -17$
Second, multiply both sides by 5. / Your problem should look like: $t - 15 = -85$
Third, add 15 to both sides. / Your problem should look like: $t = -85 + 15$
Fourth, simplify -85 + 15 to get -70. / Your problem should look like: $t = -70$

CHECKING:
$(1)/(5) t - 3 = -17$
First, let t = -70 / Your problem should look like: $(1)/(5) x -70-3=-17$
Second, simplify $(1)/(5) x -70$ to $-(1)/(5)x70$ / Your problem should look like: $-(1)/(5) x 70-3=-17$
Third, simplify $(1)/(5) x70$ to $(70)/(5)$ / Your problem should look like: $- (70)/(5) -3=-17$
Fourth, since 14 goes into 5 to get 70, simplify the fraction by 14. / Your problem should look like: $-14-3=-17$
Fifth, simplify -14 - 3 to get -17 / Your problem should look like: $-17 = -17$

Answer: t = -70

F(x) = 2/x + 7

Write steps and inverse

Answers

Answer:

y=2/(x−7)

Step-by-step explanation:

To find the inverse function, swap x and y, and solve the resulting equation for x. If the initial function is not one-to-one, then there will be more than one inverse. So, swap the variables: x=7+(2/y) for y. y=2/(x-7).

Other Questions

There is no solution to the equation sec x = 0.True or False

Divide 986÷26 by using partial quotients

$8000 is borrowed at 6.2% p.a. Simple interest for 4 years.What is the total amount owed over 4 years??

A phone company charges $25 per month, plus an installation fee of $50. If you have paid the phone company $375, how many months have you had the phone?