Advertisements
Advertisements
प्रश्न
Find the centre and radius of the following:
x2 + y2 − 6x − 8y − 24 = 0
Advertisements
उत्तर
Given equation of the circle is
x2 + y2 − 6x − 8y − 24 = 0
Comparing this equation with
x2 + y2 + 2gx + 2fy + c = 0, we get
2g = − 6, 2f = − 8 and c = − 24
∴ g = − 3, f = − 4 and c = − 24
∴ Centre of the circle = (−g, −f) = (3, 4)
and radius of the circle = `sqrt("g"^2 + "f"^2 - "c")`
= `sqrt((- 3)^2 + (- 4)^2 - (- 24))`
= `sqrt(9 + 16 + 24)`
= `sqrt(49)`
= 7.
APPEARS IN
संबंधित प्रश्न
Find the equation of the circle with centre at (2, −3) and radius 5.
Find the centre and radius of the circle:
x2 + y2 = 25
Find the centre and radius of the circle:
(x − 5)2 + (y − 3)2 = 20
Find the equation of the circle with centre at (a, b) touching the Y-axis
Find the equation of the circle with centre at (–2, 3) touching the X-axis.
Find the equation of the circle with centre at (3,1) and touching the line 8x − 15y + 25 = 0
If y = 2x is a chord of circle x2 + y2−10x = 0, find the equation of circle with this chord as diametre
Find the equation of a circle with radius 4 units and touching both the co-ordinate axes having centre in third quadrant.
Find the equation of circle (a) passing through the origin and having intercepts 4 and −5 on the co-ordinate axes
Find the equation of a circle passing through the points (1,−4), (5,2) and having its centre on the line x − 2y + 9 = 0
Find the centre and radius of the following:
x2 + y2 − 2x + 4y − 4 = 0
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
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 :
Show that the points (9, 1), (7, 9), (−2, 12) and (6, 10) are concyclic
The line 2x − y + 6 = 0 meets the circle x2 + y2 + 10x + 9 = 0 at A and B. Find the equation of circle on AB as diameter.
Answer the following :
Find the equation of the circle concentric with x2 + y2 – 4x + 6y = 1 and having radius 4 units
Answer the following :
Show that the circles touch each other externally. Find their point of contact and the equation of their common tangent:
x2 + y2 – 4x + 10y +20 = 0,
x2 + y2 + 8x – 6y – 24 = 0.
Answer the following :
Show that the circles touch each other internally. Find their point of contact and the equation of their common tangent:
x2 + y2 – 4x – 4y – 28 = 0,
x2 + y2 – 4x – 12 = 0
The centre of the circle x = 3 + 5 cos θ, y = - 4 + 5 sin θ, is ______
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 ______
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 ______.
