Question

find the equation of the circle with centre -2,1. and also passing through the point 4,3​

Answer 1

Answer:

The formula for calculating the distance between two points is:

d=√(x2−x1)2+(y2−y1)2

Substituting the values from the points in the problem gives:

d=√(3−2)2+(4−−1)2

d=√(3−2)2+(4+1)2

d=√12+52

d=√1+25

d=√26

We can now substitute the values from the center point in the problem and the radius we calculated into the formula for the equation of a circle to give:

(x−2)2+(y−−1)2=(√26)2

(x−2)2+(y+1)2=26

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Answer 2

Step-by-step explanation:

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%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 Start with the general equation of a circle.

%28x-5%29%5E2%2B%28y--3%29%5E2=r%5E2 Plug in h=5 and k=-3 (since the center is the point (h,k) ).

%28-1-5%29%5E2%2B%28-4--3%29%5E2=r%5E2 Plug in x=-1 and y=-4 (this is the point that lies on the circle, which is in the form (x,y) ).

%28-6%29%5E2%2B%28-1%29%5E2=r%5E2 Combine like terms.

36%2B1=r%5E2 Square each term.

37=r%5E2 Add.

So because h=5, k=-3, and r%5E2=37, this means that the equation of the circle with center (5,-3) that goes through the point (-1,-4) is %28x-5%29%5E2%2B%28y%2B3%29%5E2=37.