Advertisements
Advertisements
प्रश्न
Find the equation of the circle with:
Centre (a, b) and radius\[\sqrt{a^2 + b^2}\]
Advertisements
उत्तर
Here, h = a, k = b and radius = \[\sqrt{a^2 + b^2}\]
∴ Required equation of the circle:
APPEARS IN
संबंधित प्रश्न
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:
x2 + y2 − 4x + 6y = 5
Find the centre and radius of each of the following circles:
x2 + y2 − x + 2y − 3 = 0.
Find the equation of the circle whose centre is (1, 2) and which passes through the point (4, 6).
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.
Find the equation of the circle which has its centre at the point (3, 4) and touches the straight line 5x + 12y − 1 = 0.
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: 2x2 + 2y2 − 3x + 5y = 7
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 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 x + y + 3 = 0, x − y + 1 = 0 and x = 3
Find the equation of the circle concentric with the circle x2 + y2 − 6x + 12y + 15 = 0 and double of its area.
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 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 (2, −3) and (−2, 4). Find its centre and radius.
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 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.
Find the equation of the circle which circumscribes the triangle formed by the lines x = 0, y = 0 and lx + my = 1.
Write the length of the intercept made by the circle x2 + y2 + 2x − 4y − 5 = 0 on y-axis.
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.
Write the area of the circle passing through (−2, 6) and having its centre at (1, 2).
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 ______.
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 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
If the circles x2 + y2 = a and x2 + y2 − 6x − 8y + 9 = 0, touch externally, then a =
Equation of the diameter of the circle x2 + y2 − 2x + 4y = 0 which passes through the origin is
