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poppy1173
25.10.2019 •
Mathematics
Acircle is centered at the point (-7, -1) and passes through the point (8, 7).
the radius of the circle is ? units. the point (-15, ? ) lies on this circle
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Ответ:
Let the point be (-15,y)
(-15-(-7))² + (y-(-1))² = 17²
⇒ -8² + (y+1)² = 17²
⇒ 64 + (y+1)² = 289
⇒ (y+1)² = 289 - 64 = 225
⇒ y+1 = +15 or -15
⇒ y = +15-1 or -15-1
⇒ y = 14 or -16
Thus, the point can be either (-15,14) or (-15,-16)
Ответ:
Radius of the circle is, 17 units
The point can be either (-15, -16) or (-15, -14)
Step-by-step explanation:
The general equation of circle is given by:
where, r is the radius of the circle and (h, k) is the center of the circle.
As per the statement:
A circle is centered at the point (-7, -1) and passes through the point (8, 7).
⇒Center = (-7, -1)
then;
Since, the circle passes through the point (8, 7) then we have;
Solve for r:
⇒![225+64 = r^2](/tpl/images/0346/1560/e85f4.png)
⇒![279 = r^2](/tpl/images/0346/1560/c0035.png)
or
⇒the radius of the circle is, 17 units
It is given that:
The point (-15, y) lies on this circle.
Substitute the value x = -15 and solve for y
⇒![(-8)^2+(y+1)^2 = 289](/tpl/images/0346/1560/b0cd3.png)
⇒![64+(y+1)^2= 289](/tpl/images/0346/1560/51444.png)
Subtract 64 from both sides we have;
⇒![y+1 = \pm 15](/tpl/images/0346/1560/78a0e.png)
⇒y = -16 or y = -14
Therefore, the point can be either (-15, -16) or (-15, -14)
Ответ:
30 + 2(n)
30 + 2(10) = $50
30 + 2(18) = $66
30 + 2(24) = $78