मराठी

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 - Mathematics

Advertisements
Advertisements

प्रश्न

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

पर्याय

  • (3, 1)

  • x = 4, y = 1

  • x = 8, y = 2

  • none of these

MCQ

उत्तर

none of these

The end points of the diameter of a circle are (x, 3) and (3, 5).
According to the question, we have:

\[\frac{x + 3}{2} = 2, y = \frac{5 + 3}{2}\]

\[ \Rightarrow x = 1, y = 4\]

shaalaa.com
Circle - Standard Equation of a Circle
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 24: The circle - Exercise 24.6 [पृष्ठ ४०]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 24 The circle
Exercise 24.6 | Q 21 | पृष्ठ ४०

संबंधित प्रश्‍न

Find the equation of the circle with:

Centre (−2, 3) and radius 4.


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 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.


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 passing through two points on Y-axis at distances 3 from the origin and having radius 5.


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 equation of the circle passing through the points:

 (0, 0), (−2, 1) and (−3, 2)


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.


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


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 passes through the origin and cuts off intercepts aand b respectively from x and - axes.


ABCD is a square whose side is a; taking AB and AD as axes, prove that the equation of the circle circumscribing the square is x2 + y2 − a (x + y) = 0.


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 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.


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 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 centroid of an equilateral triangle is (1, 1) and its one vertex is (−1, 2), then the equation of its circumcircle is


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


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


The equation of a circle with radius 5 and touching both the coordinate axes is


The area of an equilateral triangle inscribed in the circle x2 + y2 − 6x − 8y − 25 = 0 is


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×