हिंदी

Find the Equation of the Circle Which Passes Through (3, −2), (−2, 0) and Has Its Centre on the Line 2x − Y = 3. - Mathematics

Advertisements
Advertisements

प्रश्न

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

Advertisements

उत्तर

Let the required equation of the circle be

\[x^2 + y^2 + 2gx + 2fy + c = 0\]  ...(1)
It is given that the circle passes through (3, −2), (−2, 0).
∴ \[13 + 6g - 4f + c = 0\]...(2)
\[4 - 4g + c = 0\]  ...(3)
The centre lies on the line 2x − y = 3.
∴\[- 2g + f - 3 = 0\]  ...(4)
Solving (2), (3) and (4):
\[g = \frac{3}{2}, f = 6, c = 2\]
Hence, the required equation of circle is
\[x^2 + y^2 + 3x + 12y + 2 = 0\]
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 24.2 [पृष्ठ ३२]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 24 The circle
Exercise 24.2 | Q 3 | पृष्ठ ३२

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 equation of the circle with:

Centre (aa) and radius \[\sqrt{2}\]a.


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

 (x − 1)2 + y2 = 4


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


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.


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.


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.

 


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

(5, 7), (8, 1) and (1, 3)


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 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 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.


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.


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


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 ______. 


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


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


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 (−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


Equation of the circle through origin which cuts intercepts of length a and b on axes is


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×