मराठी

The Equation X2 + Y2 + 2x − 4y + 5 = 0 Represents - Mathematics

Advertisements
Advertisements

प्रश्न

The equation x2 + y2 + 2x − 4y + 5 = 0 represents

पर्याय

  • a point

  • a pair of straight lines

  • a circle of non-zero radius

  • none of these

MCQ

उत्तर

a point

The radius of the given circle = \[\sqrt{1^2 + \left( - 2 \right)^2 - 5} = 0\]

Hence, the radius of the given circle is zero, which represents a point.

shaalaa.com
Circle - Standard Equation of a Circle
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 24: The circle - Exercise 24.6 [पृष्ठ ३९]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 24 The circle
Exercise 24.6 | Q 3 | पृष्ठ ३९

संबंधित प्रश्‍न

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:

x2 + y2 − x + 2y − 3 = 0.


Find the equation of the circle which has its centre at the point (3, 4) and touches the straight line 5x + 12y − 1 = 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 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 equation of the circle which passes through (3, −2), (−2, 0) and has its centre on the line 2x − y = 3.


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


Prove that the centres of the three circles x2 y2 − 4x − 6y − 12 = 0, x2 + y2 + 2x + 4y − 10 = 0 and x2 + y2 − 10x − 16y − 1 = 0 are collinear.


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 concentric with x2 + y2 − 4x − 6y − 3 = 0 and which touches the y-axis.


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


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.


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


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


The radius of the circle represented by the equation 3x2 + 3y2 + λxy + 9x + (λ − 6) y + 3 = 0 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 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 =


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


If the circles x2 + y2 + 2ax + c = 0 and x2 + y2 + 2by + c = 0 touch each other, then


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×