The second degree equation x2 + 4y - 2x - 4y + 2 = 0 represents
A point
An ellipse of semi-major axis 1
None of the above
If y-axis touches the circle x2 + y2 + gx + fy + = 0, then the normal at this point intersects the circle at the point
( - g, - f)
A flower-bed in the form of a sector has been fenced by a wire of 40 m length. If the flower-bed has the greatest possible area, then what is the radius of the sector ?
25m
20m
10m
5m
The two circles x2 + y2 = r2 and x2 + y2 - 10x + 16 = 0 intersect at two distinct points. Then which one of the following is correct ?
r = 2 or r = 8
What is the equation of the circle which passes through the points (3, - 2) and (- 2, 0) and having its centre on the line 2x - y - 3 = 0 ?
x
What is the maximum area of a triangle that can be inscribed in a circle of radius a ?
D.
For area of to be maximurn, triangle should be an equilateral triangle
l = length of side of equilateral triangle = a
A man running round a race course notes that the sum of the distances of two flag-posts from him is always 10 m and the distance between the flag-posts is 8 m. The area of the path he encloses is :
18 square metres
15 square metres
12 square metres
The position of the point (1, 2) relative to the ellipse 2k2 + 7 = 20 is :
Outside the ellipse
Inside the ellipse but not at the focus
On the ellipse
at the focus