ANALYTIC GEOMETRY : LINES and CIRCLES

ANALYTIC GEOMETRY : LINES and CIRCLES

1. Find the equation of the line that passes through the points of intersection of y = x + 6 with 2x + 3y = 24 and y = 2x with x + 2y = 8.
Answer : 50x + 5y = 96

2. Find the equation of the line that bisects the ( a) acute angle and ( b) the obtuse angle formed by the lines 2x – y = 3 and x – 2y = 3.
Ans. ( a) x – y = 2

3. Find the equation of the line containing the point ( 3, – 2) and ( a) parallel ( b) perpendicular to the line 2x – y + 7 = 0.
Ans. ( a) 2x – y = 8

4. Find the area of the square whose two sides are on the parallel lines
defined by 3x – 4y = 10 and 3x – 4y = 20.
Ans. 4 square units

5. Fine the equation of the circle tangent to the line 4x – 3y + 10 = 0 and having center at ( 5, 5).
Ans. X² + y² - 10x - 10y + 41 = 0

6. Determine the center and radius of the following circles:
a) x² + y² + 4x – 6y = 12
b) x²+ y² – 6x + 8y + 16 = 0

7. Find the equation of the circle tangent to the x-axis at ( 5, 0) with radius of 4 units.
( two answers)


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