Fichas
Circles
Fichas del conjunto (16)
- 1What is the general equation for a circle?(x-a)^2 + (y-b)^2 = r^2
- 2Of (x-a)^2 + (y-b)^2 = r^2 , what would be the centre point?(a,b)
- 3How do we find the exact radius of (x-a)^2 + (y-b)^2 = r^2?Square root r
- 4If we had the equation x^2+y^2+4x-8y=2, how would we find the radius and the centre?1. Complete the square for both x and y, so (x+2)^2-4 + (y-4)^2-16=2 , and then rearrange for (x-a)^2 + (y-b)^2 = r^2 format, so (x+2)^2 + (y-4)^2 = 22.
2. We now know the centre is (-2,4) and the radius is root22.
(note when we complete the square, 2^2 would be given as -4 instead of 4 in this example) - 5To find distances in and around a circle, we use....Pythagoras
- 6To find points of intersection we use....Simultaneous equations
- 7The normal is....A line through the circle passing through the centre point
- 8A tangent is....A line which scrapes the edge of a circle
- 9The normal (and or radius) meets the tangent at what angle?90 degrees
- 10To verify a point lies withing a circle, we....Sub in the coordinates to the x and y of the circles equation (x-a)^2+(y-b)^2 = r^2 and make sure it equals r^2
- 11To find the equation of a tangent, we must....Find the equation of the normal and find the perpendicular line to it.
- 12With a difficult circle question, you should always....Sketch a diagram of it
- 13If we are only given coordinates of points which pass through the circle, we can find it's equation by......1. Finding perpendicular bisector of 2 chords between points, find the intercept (centre) and generate the radius
2. Sub in coordinates to equation of a circle, expand and simplify, solve simultaneous equation and sub in a and b to new equation to find radius squares - 14A tangent would have the discriminant (when subbed in) of .....0
- 15A line which intersects a circle at 2 points would have the discriminant (when subbed in) of....>0
- 16A line which doesn't intersect the circle would have the discriminant (when subbed in) of....<0