हिंदी

Find the Coordinates of the Centre and Radius of Each of the Following Circles: X2 + Y2 + 6x − 8y − 24 = 0

Advertisements
Advertisements

प्रश्न

Find the coordinates of the centre and radius of each of the following circles:  x2 + y2 + 6x − 8y − 24 = 0

Advertisements

उत्तर

(i) The given equation can be rewritten as

\[x^2 + y^2 + 2\left( 3 \right)x - 2\left( 4 \right)y - 24 = 0\]
∴ Centre = \[\left( - 3, - 4 \right)\]
And, radius = \[\sqrt{\left( 3 \right)^2 + \left( 4 \right)^2 + 24} = \sqrt{49} = 7\]
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 1.1 | 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 (0, −1) and radius 1.


Find the equation of the circle with:

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


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.


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 touching y-axis at (0, 3) and making an intercept of 8 units on the X-axis.


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


Find the equation of the circle having (1, −2) as its centre and passing through the intersection of the lines 3x + y = 14 and 2+ 5y = 18.


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 equation of the circle passing through the points:

 (0, 0), (−2, 1) and (−3, 2)


Find the equation of the circle which passes through (3, −2), (−2, 0) and has its centre on the line 2x − y = 3.


Find the equation of the circle which passes through the points (3, 7), (5, 5) and has its centre on the line x − 4y = 1.


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  y = x + 2, 3y = 4x and 2y = 3x.


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 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.


The sides of a square are x = 6, x = 9, y = 3 and y = 6. Find the equation of a circle drawn on the diagonal of the square as its diameter.


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.


ABCD is a square whose side is a; taking AB and AD as axes, prove that the equation of the circle circumscribing the square is x2 + y2 − a (x + y) = 0.


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


Write the area of the circle passing through (−2, 6) and having its centre at (1, 2).


If 2x2 + λxy + 2y2 + (λ − 4) x + 6y − 5 = 0 is the equation of a circle, then its radius is


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


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


If the circles x2 + y2 = 9 and x2 + y2 + 8y + c = 0 touch each other, then c is equal to


The equation of the circle concentric with x2 + y2 − 3x + 4y − c = 0 and passing through (−1, −2) is


Equation of a circle which passes through (3, 6) and touches the axes is ______.


Equation of the circle with centre on the y-axis and passing through the origin and the point (2, 3) is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×