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
पर्याय
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 (−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:
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 at (3,1) and touching the line 8x − 15y + 25 = 0
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)
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 x2 + y2 − x +2y − 3 = 0
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
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 – 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 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 ______
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 ______.
Circle x2 + y2 – 4x = 0 touches ______.
The equation of a circle with centre at (1, 0) and circumference 10π units is ______.
The equation of the circle passing through the point (1, 1) and having two diameters along the pair of lines x² − y² − 2x + 4y − 3 = 0 is
