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3 years ago

Find the equation of the circle whose center and radius are given.

2 answers:

7 0

As i said before put the center instead of (h,k) in the general formula and put r=1
so (x-(-2))^2 + (y-(-5)^2 = 1
(x+2)^2 + (y+5)^2 = 1

Levart [38]3 years ago

4 0

Answer: The required equation of the circle is $x^2+y^2+4x+10y+28=0.$

Step-by-step explanation: We are given to find the equation of the circle with center (-2, -5) and radius of length 1 unit.

We know that

the standard equation of a circle with center (h, k) and radius of length r units is given by

$(x-h)^2+(y-k)^2=r^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

For the given circle, we have

center, (h, k) = (-2, -5) and radius, r = 1 units.

Therefore, from equation (i), we get

$(x-(-2))^2+(y-(-5))^2=1^2\\\\\Rightarrow (x+2)^2+(y+5)^2=1\\\\\Rightarrow x^2+4x+4+y^2+10x+25=1\\\\\Rightarrow x^2+y^2+4x+10y+29-1=0\\\\\Rightarrow x^2+y^2+4x+10y+28=0.$

Thus, the required equation of the circle is $x^2+y^2+4x+10y+28=0.$

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3 years ago

Divide: (-7x+x^2+15)÷(-3+x)

kakasveta [241]

Since the divisor is in the form (x + #) or (x - #), This can be done by synthetic division.
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Take the coefficients of the terms and follow these steps:

3 | 1 -7 15
   3 -12
___________ Bring down the 1, multiply the 3 by the 1 and place under the
   1 -4    3 -7, then add.
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   The bottom row is our answer. Since the problem started with a second power, the answer will start with a first power.
The bottom row are the coefficients of the terms and the last number is the remainder.
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3 0

3 years ago

Two joggers run 8 miles north and then 5 miles west. What is the shortest

Verdich [7]

The shortest distance they have to travel to return to their starting point is 9.4 miles.

Explanation

The joggers run 8 mile north and then runs 5 miles west. we have to calculate the shortest distance they have to travel to return to their starting point.

The distance traveled north and west respectively makes the height and base of a right angled triangle.

to find the shortest distance to the starting point, the hypotenuse has to be determined.

height h=8 miles

base b=5 miles

using pythagoras theorem

$b^2+h^2=H^2\\5^2+8^2=H^2\\25+64=H^2\\89=H^2\\\\H=\sqrt{89} =9.433=9.4 miles$

The shortest distance to the starting point is 9.4 miles

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3 years ago