1. Show that the equation 3x + 3y - 2x + y -1=0
represents a circle. Also, find its centre and radius.
Answers
Step-by-step explanation:
Equation of a circle is
(x - h)² + (y - k)² = r²
3x² + 3y² + 12x + 18y - 11 =0
Dividing both sides by 3
=> x² + y² + 4x + 6y - 11/3 = 0
=> x² + 4x + y² + 6y = 11/3
=> x² + 4x + 4 - 4 + y² + 6y + 9 - 9 = 11/3
=> (x + 2)² + (y + 3)² = 13 + 11/3
=> (x + 2)² + (y + 3)² = 50/3
=> (x + 2)² + (y + 3)² = 5² * 2 / 3
=> (x -(-2))² + (y - (-3))² = (5√2 / √3)²
Center = ( - 2 , - 3)
radius = 5√2 / √3
Hence 3x² + 3y² + 12x + 18y - 11 =0 is an equation of circle
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Step-by-step explanation:
∴r=
(
17
−1
−0)
2
+(
17
22
−0)
2
⇒r=
289
1
+
289
484
⇒r
2
=
289
485
As we know that equation of a circle whose centre at (h,k) and radius r is given by-
(x−h)
2
+(y−k)
2
=r
2
Therefore, equation of the given circle will be-
(x−(
17
−1
))
2
+(y−
17
22
)
2
=
289
485
⇒(x+
17
1
)
2
+(y−
17
22
)
2
=
289
485
⇒(17x+1)
2
+(17y−22)
2
=485
Hence the required answer is (17x+1)
2
+(17y−22)
2
=485.