Advertisements
Advertisements
प्रश्न
Find the centre and radius of the circle.
5x2 + 5y2+ 4x – 8y – 16 = 0
उत्तर
To make coefficient of x2 unity, divide the equation by 5 we get,
`x^2 + y^2 + 4/5 x - 8/5 y - 16/5 = 0`
Comparing the above equation with x2 + y2 + 2gx + 2fy + c = 0 we get,
2g = `4/5`, 2f = `-8/5`, c = `(- 16)/5`
∴ g = `2/5`, f = `- 4/5`, c = `(-16)/5`
Centre = (-g, -f) = `((-2)/5, 4/5)`
Radius = `sqrt("g"^2 + "f"^2 - "c"^2)`
`= sqrt((2/5)^2 + ((-4)/5)^2 - ((-16)/5))`
`= sqrt(4/25 + 16/25 + 16/5)`
`= sqrt((4 + 16 + 16 xx 5)/25)`
`= sqrt((20 + 80)/25)`
`= sqrt(100/25)`
`= sqrt4` = 2
APPEARS IN
संबंधित प्रश्न
Find the equation of the following circles having the centre (0,0) and radius 2 units
Find the centre and radius of the circle
x2 + y2 – 22x – 4y + 25 = 0
Find the equation of the circle passing through the points (0, 1), (4, 3) and (1, -1).
If the lines x + y = 6 and x + 2y = 4 are diameters of the circle, and the circle passes through the point (2, 6) then find its equation.
Find the values of a and b if the equation (a - 1)x2 + by2 + (b - 8)xy + 4x + 4y - 1 = 0 represents a circle.
If the circle touches the x-axis, y-axis, and the line x = 6 then the length of the diameter of the circle is:
A circle of area 9π square units has two of its diameters along the lines x + y = 5 and x – y = 1. Find the equation of the circle
Find centre and radius of the following circles
x2 + y2 – x + 2y – 3 = 0
If the equation 3x2 + (3 – p)xy + qy2 – 2px = 8pq represents a circle, find p and q. Also determine the centre and radius of the circle
Choose the correct alternative:
If the coordinates at one end of a diameter of the circle x2 + y2 – 8x – 4y + c = 0 are (11, 2) the coordinates of the other end are
