Advertisements
Advertisements
प्रश्न
Answer the following :
Find the centre and radius of the circle x2 + y2 − x +2y − 3 = 0
Advertisements
उत्तर
Comparing the equation x2 + y2 − x +2y − 3 = 0
with x2 + y2 + 2gx + 2fy + c = 0, we get,
2g = − 1, 2f = 2 and c = − 3
∴ g = `-1/2`, f = 1 and c = − 3
∴ centre of the circle = `(-"g", -"f") = (1/2, -1)`
and radius of the circle = `sqrt("g"^2 + "f"^2 - "c")`
= `sqrt((-1/2)^2 + (1)^2 - (-3))`
= `sqrt(1/4 + 1 + 3)`
= `sqrt(17)/2`.
APPEARS IN
संबंधित प्रश्न
Find the equation of the circle with centre at (−3, −2) and radius 6.
Find the centre and radius of the circle:
x2 + y2 = 25
Find the centre and radius of the circle:
`(x - 1/2)^2 + (y + 1/3)^2 = 1/36`
Find the equation of the circle with centre at (–2, 3) touching the X-axis.
Find the equation of the circle with centre on the X-axis and passing through the origin having radius 4.
Find the equation circle if the equations of two diameters are 2x + y = 6 and 3x + 2y = 4. When radius of circle is 9
Find the centre and radius of the following:
x2 + y2 − 2x + 4y − 4 = 0
Find the centre and radius of the following:
x2 + y2 − 6x − 8y − 24 = 0
Find the centre and radius of the following:
4x2 + 4y2 − 24x − 8y − 24 = 0
Show that the equation 3x2 + 3y2 + 12x + 18y − 11 = 0 represents a circle
Find the equation of the circle passing through the points (5, 7), (6, 6) and (2, −2)
Show that the points (3, −2), (1, 0), (−1, −2) and (1, −4) are concyclic
Choose the correct alternative:
Equation of a circle which passes through (3, 6) and touches the axes is ______.
Choose the correct alternative:
If the lines 2x − 3y = 5 and 3x − 4y = 7 are the diameters of a circle of area 154 sq. units, then find the equation of the circle
Choose the correct alternative:
If the lines 3x − 4y + 4 = 0 and 6x − 8y − 7 = 0 are tangents to a circle, then find the radius of the circle
Choose the correct alternative:
Area of the circle centre at (1, 2) and passing through (4, 6) is
Answer the following :
Find the centre and radius of the circle x = 3 – 4 sinθ, y = 2 – 4cosθ
Answer the following :
Find the equation of circle passing through the point of intersection of the lines x + 3y = 0 and 2x − 7y = 0 whose centre is the point of intersection of lines x + y + 1 = 0 and x − 2y + 4 = 0
Answer the following :
Find the equation of circle which passes through the origin and cuts of chords of length 4 and 6 on the positive side of x-axis and y-axis respectively
Answer the following :
Show that the points (9, 1), (7, 9), (−2, 12) and (6, 10) are concyclic
Answer the following :
Find the equation of the circle concentric with x2 + y2 – 4x + 6y = 1 and having radius 4 units
The radius of a circle is increasing uniformly at the rate of 2.5cm/sec. The rate of increase in the area when the radius is 12cm, will be ______
If x2 + (2h - 1)xy + y2 - 24x - 8y + k = 0 is the equation of the circle and 12 is the radius of the circle, then ______.
The equation of the circle with centre (4, 5) which passes through (7, 3) is ______.
The equation of circle whose diameter is the line joining the points (–5, 3) and (13, –3) is ______.
The equation of a circle with centre at (1, 0) and circumference 10π units is ______.
Let AB be a chord of the circle x2 + y2 = r2 subtending a right angle at the centre, then the locus of the centroid of the ΔPAB as P moves on the circle is ______.
