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Answer:
Step-by-step explanation:
We want to find the locus of a point such that the sum of the distance from any point P on the locus to (0, 2) and (0, -2) is 6.
First, we will need the distance formula, given by:
Let the point on the locus be P(x, y).
So, the distance from P to (0, 2) will be:
And, the distance from P to (0, -2) will be:
So sum of the two distances must be 6. Therefore:
Now, by substitution:
Simplify. We can subtract the second term from the left:
Square both sides:
We can cancel the x² terms and continue squaring:
We can cancel the y² and 4 from both sides. We can also subtract 4y from both sides. This leaves us with:
We can divide both sides by -4:
Adding 9 to both sides yields:
And, we will square both sides one final time.
Distribute:
The 36y will cancel. So:
Subtracting 4y² and 36 from both sides yields:
And dividing both sides by 45 produces:
Therefore, the equation for the locus of a point such that the sum of its distance to (0, 2) and (0, -2) is 6 is given by a vertical ellipse with a major axis length of 3 and a minor axis length of √5, centered on the origin.
Answer:
1 - Option C - 10,000
2 - 3x+5 will be 12 more than 3x-7.
Step-by-step explanation:
1) To find : With what number must 3.475817 be multiplied in order to obtain the number 34,758.17?
Solution :
The number 3.475817 is multiplied by number to obtain 34,758.17.
As we see that, the decimal is moved four places to the right.
Which means the number is multiplied by 10000.
i.e.
Therefore, option C is correct.
2) To find : How much greater is the value of 3x+5 than the value of 3x−7?
Solution ;
Assuming that x is the same value in each equation,
In order to determine the difference between the two values,
We ignore the 3x part as it is the same on both of the equations.
So, from 5 to -7 i.e. 7+5=12.
Therefore, 3x+5 will be 12 more than 3x-7.