Advertisements
Advertisements
Question
Find the coordinates of the centre and radius of each of the following circles: 2x2 + 2y2 − 3x + 5y = 7
Advertisements
Solution
The given equation can be rewritten as
∴ Centre = \[\left( \frac{3}{4}, \frac{- 5}{4} \right)\]
And, radius = \[\sqrt{\left( \frac{3}{4} \right)^2 + \left( \frac{- 5}{4} \right)^2 + \frac{7}{2}} = \sqrt{\frac{34 + 56}{16}} = \sqrt{\frac{90}{16}} = \frac{3\sqrt{10}}{4}\]
APPEARS IN
RELATED QUESTIONS
Find the equation of the circle with:
Centre (a, b) and radius\[\sqrt{a^2 + b^2}\]
Find the centre and radius of each of the following circles:
x2 + y2 − 4x + 6y = 5
Find the equation of the circle whose centre lies on the positive direction of y - axis at a distance 6 from the origin and whose radius is 4.
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 x-axis at a distance 5 from the origin and radius 6 units.
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.
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 2x + 5y = 18.
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 (x, y) 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.
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.
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 the following circle:
1/2 (x2 + y2) + x cos θ + y sin θ − 4 = 0
Find the coordinates of the centre and radius of each of the following circles: x2 + y2 − ax − by = 0
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 (3, −2), (−2, 0) and has its centre on the line 2x − y = 3.
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.
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, the end points of whose diameter are (2, −3) and (−2, 4). Find its centre and radius.
Find the equation of the circle the end points of whose diameter are the centres of the circles x2 + y2 + 6x − 14y − 1 = 0 and x2 + y2 − 4x + 10y − 2 = 0.
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 which passes through the origin and cuts off intercepts aand b respectively from x and y - axes.
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 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.
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 2x2 + λxy + 2y2 + (λ − 4) x + 6y − 5 = 0 is the equation of a circle, then its radius is
The equation x2 + y2 + 2x − 4y + 5 = 0 represents
The radius of the circle represented by the equation 3x2 + 3y2 + λxy + 9x + (λ − 6) y + 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 circle concentric with x2 + y2 − 3x + 4y − c = 0 and passing through (−1, −2) 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
Equation of the diameter of the circle x2 + y2 − 2x + 4y = 0 which passes through the origin is
If the circles x2 + y2 + 2ax + c = 0 and x2 + y2 + 2by + c = 0 touch each other, then
