हिंदी

Find the Equation of the Circle With: Centre (A, A) and Radius √ 2 A. - Mathematics

Advertisements
Advertisements

प्रश्न

Find the equation of the circle with:

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

Advertisements

उत्तर

Here, h = a, = a and radius  =\[\sqrt{2}a\]

∴ Required equation of the circle:

\[\left( x - a \right)^2 + \left( y - a \right)^2 = \left( \sqrt{2}a \right)^2\]
\[\Rightarrow x^2 + a^2 - 2ax + y^2 + a^2 - 2ay = 2 a^2 \]
\[ \Rightarrow x^2 + y^2 - 2ay - 2ax = 0\]
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 24.1 [पृष्ठ २१]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 24 The circle
Exercise 24.1 | Q 1.5 | पृष्ठ २१

संबंधित प्रश्न

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:

(x + 5)2 + (y + 1)2 = 9


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

x2 + y2 − 4x + 6y = 5


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


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 and passes through the point (2, 1).


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


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.


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.


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.


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


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.


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.


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 circumscribing the rectangle whose sides are x − 3y = 4, 3x + y = 22, x − 3y = 14 and 3x + y = 62.


The abscissae of the two points A and B are the roots of the equation x2 + 2ax − b2 = 0 and their ordinates are the roots of the equation x2 + 2px − q2 = 0. Find the equation of the circle with AB as diameter. Also, find its radius.


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


If the abscissae and ordinates of two points P and Q are roots of the equations x2 + 2ax − b2 = 0 and x2 + 2px − q2 = 0 respectively, then write the equation of the circle with PQ as diameter.


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.


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


If the equation of a circle is λx2 + (2λ − 3) y2 − 4x + 6y − 1 = 0, then the coordinates of centre are


If 2x2 + λxy + 2y2 + (λ − 4) x + 6y − 5 = 0 is the equation of a circle, then its radius 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 point (2, k) lies outside the circles x2 + y2 + x − 2y − 14 = 0 and x2 + y2 = 13 then k lies in the interval


The equation of the incircle formed by the coordinate axes and the line 4x + 3y = 6 is


If the circle x2 + y2 + 2ax + 8y + 16 = 0 touches x-axis, then the value of a is


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


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


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