$r$.","back":"$$(x-a)^2+(y-b)^2=r^2$","points":1},{"id":"77b1a539-e763-4e28-8f32-fcd656304269","cardType":"basic","front":"Identify the centre of the circle with equation $(x+5)^2+(y-2)^2=49$.","back":"$(-5,2)$","points":1},{"id":"84bdd7ca-3144-401d-ab35-49c0507e3765","cardType":"basic","front":"Identify the radius of the circle with equation $(x-2)^2+(y+1)^2=25$.","back":"5","points":1},{"id":"118dc75a-ac37-4eb4-8244-d2051417df20","cardType":"cloze","front":"To find the radius squared directly between centre $(x_1,y_1)$ and point $(x_2,y_2)$, use $r^2 = \\text{[...]}.","back":"To find the radius squared directly between centre $(x_1,y_1)$ and point $(x_2,y_2)$, use $r^2 = \\boxed{(x_2-x_1)^2+(y_2-y_1)^2}.","points":null},{"id":"599adc38-e799-47d1-bdb0-a4b1ceeb9238","cardType":"basic","front":"Why is it often unnecessary to calculate the square root of the distance when finding a circle's equation from coordinates?","back":"The standard equation uses $r^2$, not $r$.","points":1},{"id":"49b9b33a-5432-4a94-a6a0-5469293182dd","cardType":"basic","front":"Which algebraic method converts an expanded equation (e.g., $x^2+y^2+6x-8y=11$) into centre-radius form?","back":"Completing the square for $x$ and $y$ separately.","points":1},{"id":"c457f53f-0e2e-42a4-bf6f-6c7b015f58aa","cardType":"cloze","front":"After completing the square, if the right-hand side is [ ], the equation does not represent a real circle.","back":"After completing the square, if the right-hand side is negative, the equation does not represent a real circle.","points":null},{"id":"cda814c1-944c-4591-8290-90861119a7a3","cardType":"basic","front":"How do you find an unknown constant $k$ in a circle equation if given a point $(x,y)$ on the circumference?","back":"Substitute the point's coordinates into the equation and solve for $k$.","points":1},{"id":"9cf0fdf2-826a-4fa3-9659-661ed71e9bc5","cardType":"cloze","front":"To find where a circle intersects the y-axis, you must set $\\text{[...]}$.","back":"To find where a circle intersects the y-axis, you must set $\\boxed{x=0}$.","points":null},{"id":"b56f268b-126f-41d5-bebd-f6bbcbc1f286","cardType":"cloze","front":"To find where a circle intersects the x-axis, you must set $\\text{[...]}$.","back":"To find where a circle intersects the x-axis, you must set $\\boxed{y=0}$.","points":null},{"id":"00d7e17a-44e1-4434-80d7-ec5c0d01ee49","cardType":"basic","front":"Outline the steps to find the coordinates where a line $y=mx+c$ meets a circle.","back":"

Substitute the line equation into the circle equation
Solve the resulting quadratic for $x$
Substitute $x$ values back into the line equation to find $y$

","points":3},{"id":"de34f3ed-a434-439d-9534-8a438246855b","cardType":"basic","front":"At what angle does a radius meet a tangent at the point of contact?","back":"90° (perpendicular).","points":1},{"id":"8d023972-0936-419d-8402-2a34bab3f130","cardType":"basic","front":"If the gradient of a radius is $m$, what is the gradient of the tangent at that point?","back":"The negative reciprocal ($-\\frac{1}{m}$).","points":1},{"id":"d3b6900e-99c7-4746-8788-639ab8d6ea16","cardType":"cloze","front":"If a circle's radius is vertical, its tangent is [ ]; if the radius is horizontal, its tangent is vertical.","back":"If a circle's radius is vertical, its tangent is horizontal; if the radius is horizontal, its tangent is vertical.","points":null},{"id":"770c26ac-a3d0-428b-9b85-e1eb4ebc36dc","cardType":"cloze","front":"If a circle's radius is vertical, its tangent is hor

6.2 Equation of a Circle Flashcards

6.2 Equation of a Circle Flashcards

6.2 Equation of a Circle Flashcards

6.2 Equation of a Circle Flashcards