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(1.) The line
y=2x-1 passes through the centre of a circle with radius 6 units. Write down a possible equation of the circle.
sub any value of
x
BSS/Additional Mathematics/S3G3
Chapter 7: Coordinate Geometry

( $1$ .) The line $y=2 x-1$ passes through the centre of a circle with radius $6$ units. Write down a possible equation of the circle. $\newline$ sub any value of $x$ $\newline$ BSS/Additional Mathematics/S $3$ G $3$ $\newline$ Chapter $7$ : Coordinate Geometry

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Find the magnitude of a vector

Full solution

Q. (

1

.) The line

y=2 x-1

passes through the centre of a circle with radius

6

units. Write down a possible equation of the circle.

\newline

sub any value of

x

\newline

BSS/Additional Mathematics/S

3

G

3

\newline

Chapter

7

: Coordinate Geometry

Find Center Coordinates: To find the equation of the circle, we need to know the coordinates of the center of the circle. Since the center lies on the line $y=2x-1$ , we can choose any point $(x, y)$ on this line to be the center. Let's choose $x=0$ to make the calculation simple.
Substitute $x=0$ : Substitute $x=0$ into the line equation $y=2x-1$ to find the y-coordinate of the center. $\newline$ $y = 2(0) - 1$ $\newline$ $y = -1$ $\newline$ So, the center of the circle is at $(0, -1)$ .
Circle Equation Formula: The general equation of a circle with center $(h, k)$ and radius $r$ is $(x-h)^2 + (y-k)^2 = r^2$ . We know the center $(h, k)$ is $(0, -1)$ and the radius $r$ is $6$ units.
Substitute Center and Radius: Substitute the center coordinates and the radius into the circle equation to get the equation of the circle. $\newline$ $(x-0)^2 + (y-(-1))^2 = 6^2$ $\newline$ $x^2 + (y+1)^2 = 36$
Simplify Equation: Simplify the equation if necessary. In this case, the equation is already in its simplest form. $x^2 + (y+1)^2 = 36$

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