QI - The sum of the distance of a movingpoint from the points (c,0) and (-c,0) is
always 2a units. Find the equation to the locus
of the moving point.

Answers

Answer 1

Answer:

Answer:

$(x^2)/(a^2)+(y^2)/(a^2-c^2)=1$

Step-by-step explanation:

Let P be the moving point and the given points be A (c,0) and B (-c, 0). If (h, k) be the co-ordinates of any position of P on its locus then:

PA + PB = 2a

PA = 2a - PB

PA² = 4a² + PB² – 4a ∙ PB

PA² – PB² = 4a² – 4a ∙ PB

[(h - c)² +(k - 0)²] - [(h + c)² +(k - 0)²] = 4a² – 4a. PB

-4hc = 4a² – 4a∙PB

a ∙ PB = a² + hc

Taking square

a² ∙ PB² = (a² + hc)²

a² [(h + c)² + (k - 0)²] = (a² + hc)²

a² [h² + c² + 2hc + k²] = a⁴ + 2a²hc + h²c²

a²h² – h²c² + a²k² = a⁴ – a²c²

(a² – c²)h² + a²k² = a² (a² – c²)

h²/a² + k²/(a² – c²) = 1

Therefore, the required equation to the locus of P is

$(x^2)/(a^2)+(y^2)/(a^2-c^2)=1$

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Answers

Answer:

y= -3y - 1/3x

Step-by-step explanation:

-2(x + 3y) = 18 Distribute the -2 to the x + 3y

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33.52 is what percent of 8

Answers

33.52 is 419% of 8

Divide the two numbers (33.52 by 8):
$(33.52)/(8) = 4.19$

Change the decimal into a percentage by multiplying the decimal by 100:
$4.19 * 100 = 419$

Twelve pounds of beans are distributed equally into 8 bags to give out at the food bank. How many pounds of beans are in each bag

Answers

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What is the slope of the line through the points (9,2) (9,2) and (4,10)

Answers

Answer:

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Step-by-step explanation:

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Sally's cat is stuck in a tree 18 ft off the ground. The base of a ladder is placed 6 feet away from the base of the tree. What is the minimum length ladder needed to reach the cat (rounded to the nearest foot)?

Answers

Answer: 19 ft

Step-by-step explanation:

Hi, we have to apply the Pythagorean Theorem, since the tree and the ladder form a right triangle. (see attachment)

Hypotenuse squared = side squared + side squared.

Hypotenuse of a right triangle is the longest side.

Replacing with the values given:

x^2 = 18^2 + 6 ^2

Where x is the length of the ladder.( because is the longest side)

Solving for x:

√(18^2 + 6 ^2)= x

19 ft

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