As we know that the standard equation of circle is ${\bf{(x-h)^{2}+(y-k)^{2}=r^{2}}}$ , where r is the radius of circle and centre at (h,k) 

Now , as the circle passes through (2,9) so it must satisfy the above equation after putting the values of h and k respectively

${:\implies \quad \sf \{2-(-1)\}^{2}+(9-5)^{2}=r^{2}}$

${:\implies \quad \sf (3)^{2}+(4)^{2}=r^{2}}$

${:\implies \quad \sf 9+16=r^{2}}$

After raising ½ power to both sides , we will get r = +5 , -5 , but as radius can never be -ve . So r = +5 

Now , putting values in our standard equation ;

${:\implies \quad \sf \{x-(-1)\}^{2}+(y-5)^{2}=(5)^{2}}$

${:\implies \quad \bf \therefore \quad \underline{\underline{(x+1)^{2}+(y-5)^{2}=25}}}$

This is the required equation of Circle

Refer to the attachment as well !

8 0

2 years ago

If you have a spinner with 5 slots, what is the compound probability of spinning an even number, then an odd number? Expressed a

Minchanka [31]

Since the spinner has 5 slots it contains 3 odd and 2 evens,

Odds ⇒ 1, 3, 5

Evens⇒ 2,4

this can be expressed as

$\frac{2}{5} =\frac{x}{100}$ , cross multiply and we get

$5x=200$

$x=40$ %

6 0

2 years ago

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if you practice a musical instrument each day for 2/3 of an hour how many hours of practice would you get in each week?

RideAnS [48]

In order to find the answer of the given problem above, we need to make the solution below:
Given: 2/3 of an hour = practice each day
2/3 of an hour is equivalent to 40 minutes
And per week, there are 7 days. So we will multiply 40 minutes by 7, and the result is 280 minutes. Since there are 60 minutes in an hour, we divide 280 by 60 and we get 4.67 hours. Therefore, each week, you would get 4.67 hours of practice on playing a musical instrument.

3 0

2 years ago