मराठी

Find the Equation of the Circle Passing Through the Points: (0, 0), (−2, 1) and (−3, 2) - Mathematics

Advertisements
Advertisements

प्रश्न

Find the equation of the circle passing through the points:

 (0, 0), (−2, 1) and (−3, 2)

Advertisements

उत्तर

Let the required circle be

\[x^2 + y^2 + 2gx + 2fy + c = 0\]  ...(1)
It passes through (0, 0), (−2, 1) and (−3, 2).
Substituting the coordinates of these points in equation (1):
\[c = 0\] ...(2)
\[5 - 4g + 2f + c = 0\]  ...(3)
\[13 - 6g + 4f + c = 0\] ...(4)
Simplifying (2), (3) and (4):
\[g = \frac{- 3}{2}, f = \frac{- 11}{2}, c = 0\]
The equation of the required circle is
\[x^2 + y^2 - 3x - 11y = 0\]
shaalaa.com
Advanced Concept of Circle - Standard Equation of a Circle
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 24: The circle - Exercise 24.2 [पृष्ठ ३२]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 24 The circle
Exercise 24.2 | Q 2.4 | पृष्ठ ३२

संबंधित प्रश्‍न

Find the equation of the circle with:

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


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

 (x − 1)2 + y2 = 4


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

x2 + y2 − 4x + 6y = 5


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

x2 + y2 − x + 2y − 3 = 0.


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 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 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).


A circle of radius 4 units touches the coordinate axes in the first quadrant. Find the equations of its images with respect to the line mirrors x = 0 and y = 0.


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


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 equation of the circle passing through the points:

 (5, −8), (−2, 9) and (2, 1)


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


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


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 of the circle which passes through the origin and cuts off chords of lengths 4 and 6 on the positive side of the x-axis and y-axis respectively.


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, the end points of whose diameter are (2, −3) and (−2, 4). Find its centre and radius.


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 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.


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


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


Write the equation of the unit circle concentric with x2 + y2 − 8x + 4y − 8 = 0.


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.


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


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×