मराठी

Find the Equation of the Circle With:Centre (0, −1) and Radius 1. - Mathematics

Advertisements
Advertisements

प्रश्न

Find the equation of the circle with:

Centre (0, −1) and radius 1.

Advertisements

उत्तर

 Here, h = 0, = −1 and radius = 1

∴ Required equation of the circle:

\[\left( x - 0 \right)^2 + \left( y + 1 \right)^2 = \left( 1 \right)^2\]
\[\Rightarrow x^2 + y^2 + 2y = 0\]
shaalaa.com
Advanced Concept of Circle - Standard Equation of a Circle
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 24: The circle - Exercise 24.1 [पृष्ठ २१]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 24 The circle
Exercise 24.1 | Q 1.3 | पृष्ठ २१

संबंधित प्रश्‍न

Find the equation of the circle with:

Centre (a cos α, a sin α) and radius a.


Find the centre and radius of each of the following circles:

x2 + y2 − 4x + 6y = 5


Find the equation of the circle passing through the point of intersection of the lines x + 3y = 0 and 2x − 7y = 0 and whose centre is the point of intersection of the lines x + y + 1 = 0 and x − 2y + 4 = 0.


If the equations of two diameters of a circle are 2x + y = 6 and 3x + 2y = 4 and the radius is 10, find the equation of the circle.


Find the equation of a circle
which touches both the axes at a distance of 6 units from the origin.


Find the equation of a circle
which touches both the axes and passes through the point (2, 1).


Find the equation of the circle which has its centre at the point (3, 4) and touches the straight line 5x + 12y − 1 = 0.


Show that the point (xy) given by  \[x = \frac{2at}{1 + t^2}\] and \[y = a\left( \frac{1 - t^2}{1 + t^2} \right)\]  lies on a circle for all real values of t such that \[- 1 \leq t \leq 1\] where a is any given real number.

 


Find the coordinates of the centre and radius of each of the following circles: 2x2 + 2y2 − 3x + 5y = 7


Find the coordinates of the centre and radius of each of the following circles:  x2 y2 − ax − by = 0


Find the equation of the circle passing through the points:

 (5, −8), (−2, 9) and (2, 1)


Find the equation of the circle passing through the points:

 (0, 0), (−2, 1) and (−3, 2)


Show that the points (3, −2), (1, 0), (−1, −2) and (1, −4) are concyclic.


Show that the points (5, 5), (6, 4), (−2, 4) and (7, 1) all lie on a circle, and find its equation, centre and radius.


Find the equation of the circle which circumscribes the triangle formed by the lines

 x + y = 2, 3x − 4y = 6 and x − y = 0.


Find the equation of the circle which circumscribes the triangle formed by the lines  y = x + 2, 3y = 4x and 2y = 3x.


Find the equation of the circle concentric with the circle x2 + y2 − 6x + 12y + 15 = 0 and double of its area.


Find the equation of the circle the end points of whose diameter are the centres of the circles x2 + y2 + 6x − 14y − 1 = 0 and x2 + y2 − 4x + 10y − 2 = 0.


Find the equation of the circle passing through the origin and the points where the line 3x + 4y = 12 meets the axes of coordinates.


Find the equation of the circle which circumscribes the triangle formed by the lines x = 0, y = 0 and lx + my = 1.


Find the equations of the circles which pass through the origin and cut off equal chords of \[\sqrt{2}\] units from the lines y = x and y = − x.


Write the length of the intercept made by the circle x2 + y2 + 2x − 4y − 5 = 0 on y-axis.


If the abscissae and ordinates of two points P and Q are roots of the equations x2 + 2ax − b2 = 0 and x2 + 2px − q2 = 0 respectively, then write the equation of the circle with PQ as diameter.


If the radius of the circle x2 + y2 + ax + (1 − a) y + 5 = 0 does not exceed 5, write the number of integral values a.


If the equation of a circle is λx2 + (2λ − 3) y2 − 4x + 6y − 1 = 0, then the coordinates of centre are


The equation x2 + y2 + 2x − 4y + 5 = 0 represents


If the equation (4a − 3) x2 + ay2 + 6x − 2y + 2 = 0 represents a circle, then its centre is ______. 


The radius of the circle represented by the equation 3x2 + 3y2 + λxy + 9x + (λ − 6) y + 3 = 0 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


If the point (2, k) lies outside the circles x2 + y2 + x − 2y − 14 = 0 and x2 + y2 = 13 then k lies in the interval


If the point (λ, λ + 1) lies inside the region bounded by the curve \[x = \sqrt{25 - y^2}\] and y-axis, then λ belongs to the interval


The equation of a circle with radius 5 and touching both the coordinate axes is


The equation of the circle which touches the axes of coordinates and the line \[\frac{x}{3} + \frac{y}{4} = 1\] and whose centres lie in the first quadrant is x2 + y2 − 2cx − 2cy + c2 = 0, where c is equal to


If (x, 3) and (3, 5) are the extremities of a diameter of a circle with centre at (2, y), then the values of x and y are


If (−3, 2) lies on the circle x2 + y2 + 2gx + 2fy + c = 0 which is concentric with the circle x2 + y2 + 6x + 8y − 5 = 0, then c =


Equation of the diameter of the circle x2 + y2 − 2x + 4y = 0 which passes through the origin is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×