x.Exhaust.x
Retired Member
Hey guys . These questions are on the topic of co-ordinate geometry. I tried posting this thread up before which took a lot of time, but then it said: 'Invalid Link: Please notify the administrator' .
Ok back on topic. Here are the q's (Or if you happen to have Year 11 Prelim. Cambridge, refer to Exercise 5E pages 178,179 , q6, q7b), q7d), q11b), q13)a), q13)b). Please show all working out. Thank you.
1. The line y-x+h=0 is more than 1/root 2 units from the point (2,7). What range of values may h take?
2. Use the perpendicular distance formula to determine how many times each line intersects the given circle:
a) 7x+y-10=0, x^2+y^2 = 2
b) x+2y+3=0, (x+2)^2 + (y-1)^2 = 6
3. Please refer to Question 11b) on the diagram of Cambridge. If you don't have cambridge, then I'll explain what I did:
Well I found the perpendicular distance, radius and centre of the circle which was the first part of the question. Then it tells me to determine the length of the chord cut off from the line by the circle. Is the perpendicular distance of a circle equal to the chord of the circle?
4. The point P(x,y) is equidistant from the lines 2x+y-3=0 and x-2y+1=0 which intersect at A.
a) use the distance formula to show that |2x+y-3| = |x-2y+1|
b) hence find the equations of the lines that bisect the angles at A
Ok back on topic. Here are the q's (Or if you happen to have Year 11 Prelim. Cambridge, refer to Exercise 5E pages 178,179 , q6, q7b), q7d), q11b), q13)a), q13)b). Please show all working out. Thank you.
1. The line y-x+h=0 is more than 1/root 2 units from the point (2,7). What range of values may h take?
2. Use the perpendicular distance formula to determine how many times each line intersects the given circle:
a) 7x+y-10=0, x^2+y^2 = 2
b) x+2y+3=0, (x+2)^2 + (y-1)^2 = 6
3. Please refer to Question 11b) on the diagram of Cambridge. If you don't have cambridge, then I'll explain what I did:
Well I found the perpendicular distance, radius and centre of the circle which was the first part of the question. Then it tells me to determine the length of the chord cut off from the line by the circle. Is the perpendicular distance of a circle equal to the chord of the circle?
4. The point P(x,y) is equidistant from the lines 2x+y-3=0 and x-2y+1=0 which intersect at A.
a) use the distance formula to show that |2x+y-3| = |x-2y+1|
b) hence find the equations of the lines that bisect the angles at A