Advertisements
Advertisements
प्रश्न
Write the equation of the unit circle concentric with x2 + y2 − 8x + 4y − 8 = 0.
Advertisements
उत्तर
The centre of the circle x2 + y2 − 8x + 4y − 8 = 0 is (4, −2).
The radius of the unit circle is 1.
∴ Required equation of circle:
\[\left( x - 4 \right)^2 + \left( y + 2 \right)^2 = 1\],
\[\Rightarrow\] \[x^2 + y^2 - 8x + 4y + 19 = 0\]
APPEARS IN
संबंधित प्रश्न
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 (a, a) and radius \[\sqrt{2}\]a.
Find the centre and radius of each of the following circles:
(x + 5)2 + (y + 1)2 = 9
Find the equation of the circle whose centre is (1, 2) and which passes through the point (4, 6).
A circle whose centre is the point of intersection of the lines 2x − 3y + 4 = 0 and 3x + 4y− 5 = 0 passes through the origin. Find its equation.
Find the equations of the circles touching y-axis at (0, 3) and making an intercept of 8 units on the X-axis.
Find the equations of the circles passing through two points on Y-axis at distances 3 from the origin and having radius 5.
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 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:
(5, 7), (8, 1) and (1, 3)
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.
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 concentric with the circle x2 + y2 − 6x + 12y + 15 = 0 and double of its area.
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 which passes through the points (2, 3) and (4,5) and the centre lies on the straight line y − 4x + 3 = 0.
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.
Find the equation of the circle which passes through the origin and cuts off intercepts aand b respectively from x and y - axes.
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.
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.
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 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 concentric with x2 + y2 − 3x + 4y − c = 0 and passing through (−1, −2) is
The area of an equilateral triangle inscribed in the circle x2 + y2 − 6x − 8y − 25 = 0 is
If (−3, 2) lies on the circle x2 + y2 + 2gx + 2fy + c = 0 which is concentric with the circle x2 + y2 + 6x + 8y − 5 = 0, then c =
If the circles x2 + y2 + 2ax + c = 0 and x2 + y2 + 2by + c = 0 touch each other, then
Equation of a circle which passes through (3, 6) and touches the axes is ______.
