हिंदी

Find the Coordinates of the Centre and Radius of Each of the Following Circles: X2 + Y2 − Ax − by = 0

Advertisements
Advertisements

प्रश्न

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

Advertisements

उत्तर

The given equation can be rewritten as

\[x^2 + y^2 - \frac{2ax}{2} - \frac{2by}{2} = 0\]

∴ Centre = \[\left( \frac{a}{2}, \frac{b}{2} \right)\]

And, radius =\[\sqrt{\left( \frac{a}{2} \right)^2 + \left( \frac{b}{2} \right)^2} = \frac{1}{2}\sqrt{a^2 + b^2}\]

shaalaa.com
Advanced Concept of Circle - Standard Equation of a Circle
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 24: The circle - Exercise 24.2 [पृष्ठ ३१]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 24 The circle
Exercise 24.2 | Q 1.4 | पृष्ठ ३१

संबंधित प्रश्न

Find the equation of the circle with:

Centre (−2, 3) and radius 4.


Find the equation of the circle with:

Centre (ab) and radius\[\sqrt{a^2 + b^2}\]


Find the equation of the circle with:

Centre (0, −1) and radius 1.


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

x2 + y2 − x + 2y − 3 = 0.


Find the equation of the circle whose centre is (1, 2) and which passes through the point (4, 6).


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
passing through the origin, radius 17 and ordinate of the centre is −15.


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


Find the equations of the circles passing through two points on Y-axis at distances 3 from the origin and having radius 5.


If the lines 2x  3y = 5 and 3x − 4y = 7 are the diameters of a circle of area 154 square units, then obtain the equation of the circle.


The circle x2 + y2 − 2x − 2y + 1 = 0 is rolled along the positive direction of x-axis and makes one complete roll. Find its equation in new-position.


One diameter of the circle circumscribing the rectangle ABCD is 4y = x + 7. If the coordinates of A and B are (−3, 4) and (5, 4) respectively, find the equation of the circle.


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


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 + + 3 = 0, x − y + 1 = 0 and x = 3


Prove that the radii of the circles x2 + y2 = 1, x2 + y2 − 2x − 6y − 6 = 0 and x2 + y2 − 4x − 12y − 9 = 0 are in A.P.


Find the equation to the circle which passes through the points (1, 1) (2, 2) and whose radius is 1. Show that there are two such circles.


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.


Find the equation of the circle circumscribing the rectangle whose sides are x − 3y = 4, 3x + y = 22, x − 3y = 14 and 3x + y = 62.


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 whose diameter is the line segment joining (−4, 3) and (12, −1). Find also the intercept made by it on y-axis.


The line 2x − y + 6 = 0 meets the circle x2 + y2 − 2y − 9 = 0 at A and B. Find the equation of the circle on AB as diameter.


Write the coordinates of the centre of the circle passing through (0, 0), (4, 0) and (0, −6).


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


The number of integral values of λ for which the equation x2 + y2 + λx + (1 − λ) y + 5 = 0 is the equation of a circle whose radius cannot exceed 5, 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 centroid of an equilateral triangle is (1, 1) and its one vertex is (−1, 2), then the equation of its circumcircle is


If the circle x2 + y2 + 2ax + 8y + 16 = 0 touches x-axis, then the value of a is


The equation of the circle passing through the origin which cuts off intercept of length 6 and 8 from the axes is


The circle x2 + y2 + 2gx + 2fy + c = 0 does not intersect x-axis, if


The area of an equilateral triangle inscribed in the circle x2 + y2 − 6x − 8y − 25 = 0 is


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


The equation of the circle circumscribing the triangle whose sides are the lines y = x + 2, 3y = 4x, 2y = 3x is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×