Question

If the equation of a circle is (x + 5)2 + (y - 7)2 = 36, its center point is (5, 7) (-5, 7) (5, -7)

If the equation of a circle is (x + 5)2 + (y - 7)2 = 36, its radius is 6 16 36
If the equation of a circle is (x - 2)2 + (y - 6)2 = 4, the center is point (2, 6).
a. True
b. False
The distance between A (-5, 3) and B(5, 3) is. 3 6 10

Answer 1

Hello,
1): its center point is (-5,7). Answer B
2):radius is 6 Answer A
3) Anwser A true
4)|AB|=√((5+5)²+(3-3)²)=10 Answer C

Answer 2

Part 1. Center point is ( -5 , 7 ).

Part 2. Radius is 6

Part 3. False

Parts 4. Distance between A & B is 10.

Explanation:

Standard Equation of circle is ,

( x - h )² + ( y - k )² = r²

where, ( h , k ) is coordinate of center of circle and r is radius of circle.

Part 1.

Comparing with standard equation of circle we get,

Coordinate of center of circle = ( -5 , 7 )

Thus, 2nd Option is correct.

Part 2.

Comparing with standard equation of circle we get,

radius of circle = 6

Thus, 1st Option is correct.

Part 3.

Comparing with standard equation of circle we get,

Coordinate of center of circle = ( 2 , 3 )

Thus, False.

Part 1.

Distance between two point given by
`√((x_2-x_1)^2+(y_1-y_1)^2)`

Distance between A( -5 , 3 ) & B ( 5 , 3 ) =
`√((-5-5)^2+(3-3)^2)`

=
`√((-10)^2+0^2)`

=
`10`

Thus, 3rd Option is correct.