English

Find the Equation of the Circle Which Circumscribes the Triangle Formed by the Lines X = 0, Y = 0 and Lx + My = 1.

Advertisements
Advertisements

Question

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

Advertisements

Solution

The coordinates of A and B are

\[\left( 0, \frac{1}{m} \right) and \left( \frac{1}{l}, 0 \right)\]
Here, the end points of the diameter of the circumcircle are A and B.
∴ Required equation of the circle:
\[\left( x - 0 \right)\left( x - \frac{1}{l} \right) + \left( y - \frac{1}{m} \right)\left( y - 0 \right) = 0\]
\[\Rightarrow x^2 - \frac{x}{l} + y^2 - \frac{y}{m} = 0\]
shaalaa.com
Advanced Concept of Circle - Standard Equation of a Circle
  Is there an error in this question or solution?
Chapter 24: The circle - Exercise 24.3 [Page 38]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 24 The circle
Exercise 24.3 | Q 11 | Page 38

RELATED QUESTIONS

Find the equation of the circle with:

Centre (0, −1) and radius 1.


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:

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


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


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.


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.


If the line 2x − y + 1 = 0 touches the circle at the point (2, 5) and the centre of the circle lies on the line x + y − 9 = 0. Find the equation of the circle.


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


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 x + + 3 = 0, x − y + 1 = 0 and x = 3


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 of the circle concentric with the circle x2 + y2 − 6x + 12y + 15 = 0 and double of its area.


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


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


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


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 point (2, k) lies outside the circles x2 + y2 + x − 2y − 14 = 0 and x2 + y2 = 13 then k lies in the interval


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 the circles x2 + y2 = a and x2 + y2 − 6x − 8y + 9 = 0, touch externally, then a =


If (x, 3) and (3, 5) are the extremities of a diameter of a circle with centre at (2, y), then the values of x and y are


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


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


The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×