Advertisements
Advertisements
प्रश्न
Find the coordinates of the centre and radius of each of the following circles: x2 + y2 − ax − by = 0
Advertisements
उत्तर
The given equation can be rewritten as
∴ Centre = \[\left( \frac{a}{2}, \frac{b}{2} \right)\]
And, radius =\[\sqrt{\left( \frac{a}{2} \right)^2 + \left( \frac{b}{2} \right)^2} = \frac{1}{2}\sqrt{a^2 + b^2}\]
APPEARS IN
संबंधित प्रश्न
Find the equation of the circle with:
Centre (0, −1) and radius 1.
Find the centre and radius of each of the following circles:
(x + 5)2 + (y + 1)2 = 9
Find the equation of the circle which touches the axes and whose centre lies on x − 2y = 3.
Find the equations of the circles passing through two points on Y-axis at distances 3 from the origin and having radius 5.
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 equation of the circle passing through the points:
(5, −8), (−2, 9) and (2, 1)
Find the equation of the circle passing through the points:
(0, 0), (−2, 1) and (−3, 2)
Find the equation of the circle which passes through the points (3, 7), (5, 5) and has its centre on the line x − 4y = 1.
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.
Find the equation of the circle which circumscribes the triangle formed by the lines x + y + 3 = 0, x − y + 1 = 0 and x = 3
Find the equation of the circle which circumscribes the triangle formed by the lines 2x + y − 3 = 0, x + y − 1 = 0 and 3x + 2y − 5 = 0
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 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.
The sides of a square are x = 6, x = 9, y = 3 and y = 6. Find the equation of a circle drawn on the diagonal of the square as its diameter.
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.
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 length of the intercept made by the circle x2 + y2 + 2x − 4y − 5 = 0 on y-axis.
Write the equation of the unit circle concentric with x2 + y2 − 8x + 4y − 8 = 0.
If the equation of a circle is λx2 + (2λ − 3) y2 − 4x + 6y − 1 = 0, then the coordinates of centre are
The radius of the circle represented by the equation 3x2 + 3y2 + λxy + 9x + (λ − 6) y + 3 = 0 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
The equation of the incircle formed by the coordinate axes and the line 4x + 3y = 6 is
If the point (λ, λ + 1) lies inside the region bounded by the curve \[x = \sqrt{25 - y^2}\] and y-axis, then λ belongs to the interval
If the circle x2 + y2 + 2ax + 8y + 16 = 0 touches x-axis, then the value of a is
The equation of a circle with radius 5 and touching both the coordinate axes is
The equation of the circle passing through the origin which cuts off intercept of length 6 and 8 from the axes is
The equation of the circle which touches the axes of coordinates and the line \[\frac{x}{3} + \frac{y}{4} = 1\] and whose centres lie in the first quadrant is x2 + y2 − 2cx − 2cy + c2 = 0, where c is equal to
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
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
