Advertisements
Advertisements
प्रश्न
Choose the correct alternative:
The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is
विकल्प
x2 + y2 = 9a2
x2 + y2 = 16a2
x2 + y2 = 4a2
x2 + y2 = a2
Advertisements
उत्तर
x2 + y2 = 4a2
Explanation;
Since the triangle is equilateral.
∴ The centroid of the triangle is same as the circumcentre;
and radius of the circumcircle = `2/3("median")`
= `2/3(3"a")`
= 2a
Hence, the equation of the circumcircle whose centre is at (0, 0) and radius 2a is x2 + y2 = 4a2.
APPEARS IN
संबंधित प्रश्न
Find the equation of the circle with centre at origin and radius 4.
Find the equation of the circle with centre at (−3, −2) and radius 6.
Find the equation of the circle with centre at (2, −3) and radius 5.
Find the centre and radius of the circle:
(x − 5)2 + (y − 3)2 = 20
Find the equation of the circle with centre on the X-axis and passing through the origin having radius 4.
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 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 − 6x − 8y − 24 = 0
Find the centre and radius of the following:
4x2 + 4y2 − 24x − 8y − 24 = 0
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 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
Choose the correct alternative:
If a circle passes through the point (0, 0), (a, 0) and (0, b) then find the co-ordinates of its centre
Answer the following :
Find the centre and radius of the circle x = 3 – 4 sinθ, y = 2 – 4cosθ
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 + 19 = 0,
x2 + y2 + 2x + 8y – 23 = 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
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 – 12y + 4 = 0,
x2 + y2 – 2x – 4y + 4 = 0
Answer the following :
Find the length of the tangent segment drawn from the point (5, 3) to the circle x2 + y2 + 10x – 6y – 17 = 0
If 2x - 4y = 9 and 6x - 12y + 7 = 0 are the tangents of same circle, then its radius will be ______
If one of the diameters of the curve x2 + y2 - 4x - 6y + 9 = 0 is a chord of a circle with centre (1, 1), then the radius of this circle is ______
If the radius of a circle increases from 3 cm to 3.2 cm, then the increase in the area of the circle 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 circle whose diameter is the line joining the points (–5, 3) and (13, –3) is ______.
Circle x2 + y2 – 4x = 0 touches ______.
The equation of a circle with centre at (1, 0) and circumference 10π units is ______.
