Advertisements
Advertisements
प्रश्न
Find the equation of the circle with centre at (3,1) and touching the line 8x − 15y + 25 = 0
Advertisements
उत्तर
The centre of the circle is (3, 1) and it is touching the line 8x − 15y + 25 = 0.
∴ radius = perpendicular distance from (3, 1) to the line 8x − 15y + 25 = 0
= `|(8(3) + (-15)(1) + 25)/sqrt(8^2 + (-15)^2)|`
= `|(24 - 15 + 25)/sqrt(64 + 225)|`
= `|34/17|`
= 2
∴ the equation of the circle is
(x − 3)2 + (y − 1)2 = 22
∴ x2 − 6x + 9 + y2 − 2y + 1 = 4
∴ x2 + y2 − 6x − 2y + 6 = 0
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, −3) passing through the point (−3, −6)
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 centre and radius of the circle:
`(x - 1/2)^2 + (y + 1/3)^2 = 1/36`
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 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 − 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
Show that the points (3, −2), (1, 0), (−1, −2) and (1, −4) are concyclic
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:
Find the equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y − 4x + 3 = 0
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 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
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 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
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 ______
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 ______.
