Question

${\rm{\red{\underline{\underline{\huge{QuesTion}}}}}} \huge{\pink{࿐}}$
Find the equation of the circle passing through the Points (4, 1)and (6, 5) and whose centre is on the line is 4x + y = 16
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Answer 1

Answer:

Given points,

(4,1),(6,5)

equation of circle (x−h)2+(y−k)2=r2

⇒(4−h)2+(1−k)2=r2 (1)

⇒(6−h)2+(5−k)2=r2 (2)

solving the above 2 equations, we get,

h+2k=11 (3)

given, 4h+k=16 (4)

solving the above 2 equations, we get,

h=3,k=4

substituting the above values in (1), we get,

(4−3)2+(1−4)2=r2

r=10

Hence, the equation is,

(x−3)2+(y−4)2=(10)2

x2+y2−6x−8y+15=0

Radhe Radhe

Answer 2

Step-by-step explanation:

Given points,

$\looparrowright$$\sf\color{red}(4,1),(6,5)$

$\looparrowright$

equation of circle

$\sf\color{pink}(x-h)2+(y-k)2=r2$

$\looparrowright$$\sf\color{purple}- (4-h)2+(1-k)2=r2 (1)$

$\looparrowright$$\sf\color{teal}(6-h)2+(5-k)2=r2 (2)$

$\looparrowright$$\sf\color{red}h+2k=11 (3)$

$\looparrowright$$\sf\color{red}given, 4h+k=16 (4)$

$\looparrowright$$\sf\color{red}h=3,K=4$

$\looparrowright$$\sf\color{red}(4-3)2+(1-4)2=r2$

$\looparrowright$$\sf\color{red}r=10$

$\looparrowright$$\sf\color{red}46 14 1 97%$

$\looparrowright$$\sf\color{red}142$

$\looparrowright$$\sf\color{red}8$

$\looparrowright$$\sf\color{red}x 5.0$

$\looparrowright$$\sf\color{red}(x-3)2+(y-4)2=(10)2[$

$\looparrowright$$\sf\color{red}X2+y2-6x-8y+15=0$