Circle (Conic)

||x^2+ y^2= r^2||

where
||r=\text{radius of a circle}||

1. Find the value of parameter |\color{#3a9a38}r,| the circle’s radius. If necessary, substitute |x| and |y| with a point on the circle and solve the equation.

2. Write the equation of the circle.

Find the equation of the circle centred at the origin that passes through point |(7,-3).|

1. Place the centre of the circle at the origin of the Cartesian plane.

2. Use the equation to find parameter |\color{#3a9a38}r|.

3. Starting from the centre, use a compass to sketch a circle whose radius is equal to |\color{#3a9a38}r.|

Sketch the circle of the equation |x^2+y^2=36.|

||(x-h)^2+(y-k)^2= r^2||
where
||\begin{align} r&=\text{radius of the circle}\\ (h,k)&=\text{coordinates of the circle’s centre}\end{align}||

1. Find the values of parameters |\color{#FF55C3}h| and |\color{#560FA5}k| from the coordinates of the circle’s centre.

2. Find the value of parameter |\color{#3a9a38}r,| the radius of the circle. If necessary, substitute |x| and |y| with a point on the circle. Then, solve the equation.

3. Write the equation of the circle.

Find the equation of a circle which passes through points |(-1, 0)| and |(-1, 4).|

1. Identify parameters |\color{#FF55C3}h| and |\color{#560FA5}k| in the equation and place the centre of the circle.

2. Determine parameter |\color{#3a9a38}r| in the equation.

3. Starting from the centre, use a compass to sketch a circle whose radius is equal to |\color{#3a9a38}r.|

Sketch the circle with the equation: |(x+4)^2+(y-3)^2=16.|

1. Find the slope of the line that passes through the centre of the circle and the point of tangency.

2. Find the slope of the tangent line using the relationship between two perpendicular lines.

3. Find the y-intercept of the tangent line using its slope and the coordinates of the point of tangency.

4. Write the tangent line’s equation.

Find the equation of the line tangent to the circle with the following equation: |(x+1)^2+(y-2)^2=25| at the point |(2,6).|