हिंदी

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. - Mathematics

Advertisements
Advertisements

प्रश्न

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.

Advertisements

उत्तर

According to the question:
Sides of the square are x = 6, x = 9, y = 3 and y = 6.
The vertices of the square are (6, 6), (9, 6), (9, 3) and (6, 3).
And, the vertices of two diagonals are (6, 6), (9, 3) and (9, 6), (6, 3).
Hence, the equation of the circle is \[\left( x - 6 \right)\left( x - 9 \right) + \left( y - 6 \right)\left( y - 3 \right)\] or

\[x^2 + y^2 - 15x - 9y + 72 = 0\]
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 24.3 [पृष्ठ ३७]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 24 The circle
Exercise 24.3 | Q 3 | पृष्ठ ३७

संबंधित प्रश्न

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 centre and radius of each of the following circles:

x2 + y2 − 4x + 6y = 5


Find the equation of the circle whose centre lies on the positive direction of - axis at a distance 6 from the origin and whose radius is 4.


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


Find the equation of the circle which touches the axes and whose centre lies on x − 2y = 3.


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.


If the line y = \[\sqrt{3}\] x + k touches the circle x2 + y2 = 16, then find the value of k


If the lines 3x − 4y + 4 = 0 and 6x − 8y − 7 = 0 are tangents to a circle, then find the radius of  the circle.


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.

 


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 the following circle:

1/2 (x2 + y2) + x cos θ + y sin θ − 4 = 0


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


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


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 concentric with x2 + y2 − 4x − 6y − 3 = 0 and which touches the y-axis.


If a circle passes through the point (0, 0),(a, 0),(0, b) then find the coordinates of its centre.


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


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 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 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


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 circle through origin which cuts intercepts of length a and b on 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×