English

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

Advertisements
Advertisements

Question

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

Options

  • a point

  • a pair of straight lines

  • a circle of non-zero radius

  • none of these

MCQ
Advertisements

Solution

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
Advanced Concept of Circle - Standard Equation of a Circle
  Is there an error in this question or solution?
Chapter 24: The circle - Exercise 24.6 [Page 39]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 24 The circle
Exercise 24.6 | Q 3 | Page 39

RELATED QUESTIONS

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

x2 + y2 − 4x + 6y = 5


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 at a distance of 6 units from the origin.


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


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. 


The circle x2 + y2 − 2x − 2y + 1 = 0 is rolled along the positive direction of x-axis and makes one complete roll. Find its equation in new-position.


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 each of the following circles:  x2 + y2 + 6x − 8y − 24 = 0


Find the coordinates of the centre and radius of each of the following circles: 2x2 + 2y2 − 3x + 5y = 7


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


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 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.


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.


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.


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.


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


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


If the equation (4a − 3) x2 + ay2 + 6x − 2y + 2 = 0 represents a circle, then its centre 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 centroid of an equilateral triangle is (1, 1) and its one vertex is (−1, 2), then the equation of its circumcircle is


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 =


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


Equation of the circle with centre on the y-axis and passing through the origin and the point (2, 3) 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×