Find the equation for the circle with a diameter whose endpoints are (-5, -3) and (3,2).
1 answer:
Answer:
(x +1)^2 +(y +0.5)^2 = 22.25
Step-by-step explanation:
The center of the circle is the midpoint of the diameter, so is ...
(h, k) = ((-5, -3) +(3, 2))/2 = (-5+3, -3+2)/2 = (-1, -1/2)
The circle formula is then ...
(x -h)^2 +(y -k)^2 = r^2
(x -(-1))^2 +(y -(-1/2))^2 = r^2
We can find r^2 by substituting one of the points for (x, y).
(3 +1)^2 +(2 +1/2)^2 = r^2 = 16 +6.25 = 22.25
Then the circle equation is ...
(x +1)^2 +(y +0.5)^2 = 22.25
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Answer:
Step-by-step explanation:
Solving for x means you have to factor. First factor out the GCF of 2 to get:
and now we'll factor using the regular old method of ac and then factoring by grouping. In our polynomial, a = 3, b = 1, c = -6. Therefore, a times c is 3 * -6 which is -18. We need some combinations of the factors of 18 that will add to give us 1, the b term in the middle. The factors of 18 are:
1, 18
2, 9
3, 6 and that's it. Hm...it seems that won't work, so let's throw this into the quadratic formula, going back to the original and a = 6, b = 2 and c = -12:
and
and
and
and
which finally simplifies to
No wonder that didn't factor using the traditional method of factoring! We could have found that out by finding first the value of the discriminant, but oh well!