Advertisements
Advertisements
प्रश्न
Answer the following :
Find the centre and radius of the circle x = 3 – 4 sinθ, y = 2 – 4cosθ
Advertisements
उत्तर
Given, x = 3 – 4 sinθ, y = 2 – 4cosθ
∴ x – 3 –4 sinθ, y –2 = – 4cosθ
On squaring and adding, we get
(x – 3)2 + (y – 2)2 = (–4 sinθ)2 + (–4 cosθ)2
∴ (x – 3)2 + (y – 2)2 = 16sin2θ + 16cos2θ
∴ (x – 3)2 + (y – 2)2 = 16(sin2θ + cos2θ)
∴ (x – 3)2 + (y – 2)2 = 16(1)
∴ (x – 3)2 + (y – 2)2 = 16
∴ (x – 3)2 + (y – 2)2 = 42
Comparing this equation with
(x – h)2 + (y – k)2 = r2, we get
h = 3, k = 2, r = 4
∴ Centre of the circle is (3, 2) and radius is 4.
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 (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 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 of the circle with centre at (3,1) and touching the line 8x − 15y + 25 = 0
Find the centre and radius of the following:
4x2 + 4y2 − 24x − 8y − 24 = 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 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
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
Answer the following :
Find the centre and radius of the circle x2 + y2 − x +2y − 3 = 0
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 :
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 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 :
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 equation of the circle with centre (4, 5) which passes through (7, 3) 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 ______.
